% VLDB.CLS - Version 1.8c
%
% based on:
% SIG-ALTERNATE.CLS - VERSION 1.8
% "COMPATIBLE" WITH THE "ACM_PROC_ARTICLE-SP.CLS" V2.7SP
% Gerald Murray July 26th. 2005
% 
% ---- Start of 'updates'  ----
%
% Allowance made to switch default fonts between those systems using
% METAFONT and those using 'Type 1' or 'Truetype' fonts.
% See LINE NUMBER 252 for details.
% Also provided for enumerated/annotated Corollaries 'surrounded' by
% enumerated Theorems (line 841).
% Gerry November 11th. 1999
%
% Made the Permission Statement / Conference Info / Copyright Info
% 'user definable' in the source .tex file OR automatic if
% not specified.
%
% Georgia fixed bug in sub-sub-section numbering in paragraphs (July 29th. 2002)
% JS/GM fix to vertical spacing before Proofs (July 30th. 2002)
%
% Footnotes inside table cells using \minipage (Oct. 2002)
%
% Enforced 'US letter' page size and updated PVLDB copyright  (UR, Oct 2010)
%
% Made the file template-able, so vol/no information can be dynmacally generated. (AhmetSacan, Sep 2012)
%
% Added widow line penalties. (AhmetSacan, Sep 2012)
% ---- End of 'updates' ----
%
\def\fileversion{v1.8c}         % for VLDB's and ACM's tracking purposes
\def\filedate{July 26, 2005}    % Gerry Murray's tracking data
\def\docdate {Tuesday 26th. July 2005} % Gerry Murray (with deltas to doc}
\usepackage[pdftex,letterpaper]{geometry} % fixed to US letter size for output (since version 1.8c - UR 2010)
\usepackage{epsfig}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
%
% VLDB DOCUMENT STYLE
% based on ACM's sig-alternate.cls, modified 31 Oct 2010 for PVLDB,
% with VLDB-specific copyright notice and fixed US letter paper size.
%
% SIG-ALTERNATE DOCUMENT STYLE
% G.K.M. Tobin August-October 1999
%    adapted from ARTICLE document style by Ken Traub, Olin Shivers
%    also using elements of esub2acm.cls
% HEAVILY MODIFIED, SUBSEQUENTLY, BY GERRY MURRAY 2000
% ARTICLE DOCUMENT STYLE -- Released 16 March 1988
%    for LaTeX version 2.09
% Copyright (C) 1988 by Leslie Lamport
%
%
%%% sig-alternate.cls is an 'ALTERNATE' document style for producing
%%% two-column camera-ready pages for ACM conferences.
%%% THIS FILE DOES NOT STRICTLY ADHERE TO THE SIGS (BOARD-ENDORSED)
%%% PROCEEDINGS STYLE. It has been designed to produce a 'tighter'
%%% paper in response to concerns over page budgets.
%%% The main features of this style are:
%%%
%%% 1)  Two columns.
%%% 2)  Side and top margins of 4.5pc, bottom margin of 6pc, column gutter of
%%%     2pc, hence columns are 20pc wide and 55.5pc tall.  (6pc =3D 1in, approx)
%%% 3)  First page has title information, and an extra 6pc of space at the
%%%     bottom of the first column for the ACM copyright notice.
%%% 4)  Text is 9pt on 10pt baselines; titles (except main) are 9pt bold.
%%% 5)  US letter paper size (since v1.8c)
%%%
%%%
%%% There are a few restrictions you must observe:
%%%
%%% 1)  You cannot change the font size; ACM wants you to use 9pt.
%%% 3)  You must start your paper with the \maketitle command.  Prior to the
%%%     \maketitle you must have \title and \author commands.  If you have a
%%%     \date command it will be ignored; no date appears on the paper, since
%%%     the proceedings will have a date on the front cover.
%%% 4)  Marginal paragraphs, tables of contents, lists of figures and tables,
%%%     and page headings are all forbidden.
%%% 5)  The `figure' environment will produce a figure one column wide; if you
%%%     want one that is two columns wide, use `figure*'.
%%%
%
%%% Copyright Space:
%%% This style automatically reserves 1" blank space at the bottom of page 1/
%%% column 1.  This space can optionally be filled with some text using the
%%% \toappear{...} command.  If used, this command must be BEFORE the \maketitle
%%% command.  If this command is defined AND [preprint] is on, then the
%%% space is filled with the {...} text (at the bottom); otherwise, it is
%%% blank.  If you use \toappearbox{...} instead of \toappear{...} then a
%%% box will be drawn around the text (if [preprint] is on).
%%%
%%% A typical usage looks like this:
%%%     \toappear{To appear in the Ninth AES Conference on Medievil Lithuanian
%%%               Embalming Technique, June 1991, Alfaretta, Georgia.}
%%% This will be included in the preprint, and left out of the conference
%%% version.
%%%
%%% WARNING:
%%% Some dvi-ps converters heuristically allow chars to drift from their
%%% true positions a few pixels. This may be noticeable with the 9pt sans-serif
%%% bold font used for section headers.
%%% You may turn this hackery off via the -e option:
%%%     dvips -e 0 foo.dvi >foo.ps
%%%
\typeout{Document Class 'vldb' - based on 'sig-alternate' <26th. July '05>.  Modified by G.K.M. Tobin/Gerry Murray}
\typeout{Based in part upon document Style `acmconf' <22 May 89>. Hacked 4/91 by}
\typeout{shivers@cs.cmu.edu, 4/93 by theobald@cs.mcgill.ca}
\typeout{Excerpts were taken from (Journal Style) 'esub2acm.cls'.}
\typeout{****** Bugs/comments/suggestions/technicalities to Gerry Murray -- murray@hq.acm.org ******}
\typeout{Questions on the style, SIGS policies, etc. to Adrienne Griscti griscti@acm.org}
\oddsidemargin 4.5pc
\evensidemargin 4.5pc
\advance\oddsidemargin by -1in  % Correct for LaTeX gratuitousness
\advance\evensidemargin by -1in % Correct for LaTeX gratuitousness
\marginparwidth 0pt             % Margin pars are not allowed.
\marginparsep 11pt              % Horizontal space between outer margin and
                                % marginal note

                                % Top of page:
\topmargin 4.5pc                % Nominal distance from top of page to top of
                                % box containing running head.
\advance\topmargin by -1in      % Correct for LaTeX gratuitousness
\headheight 0pt                 % Height of box containing running head.
\headsep 0pt                    % Space between running head and text.
                                % Bottom of page:
\footskip 30pt                  % Distance from baseline of box containing foot
                                % to baseline of last line of text.
\@ifundefined{footheight}{\newdimen\footheight}{}% this is for LaTeX2e
\footheight 12pt                % Height of box containing running foot.

%% Must redefine the top margin so there's room for headers and
%% page numbers if you are using the preprint option. Footers
%% are OK as is. Olin.
\advance\topmargin by -37pt     % Leave 37pt above text for headers
\headheight 12pt                % Height of box containing running head.
\headsep 25pt                   % Space between running head and text.

\textheight 666pt       % 9 1/4 column height
\textwidth 42pc         % Width of text line.
                        % For two-column mode:
\columnsep 2pc          %    Space between columns
\columnseprule 0pt      %    Width of rule between columns.
\hfuzz 1pt              % Allow some variation in column width, otherwise it's
                        % too hard to typeset in narrow columns.

\footnotesep 5.6pt      % Height of strut placed at the beginning of every
                        % footnote =3D height of normal \footnotesize strut,
                        % so no extra space between footnotes.

\skip\footins 8.1pt plus 4pt minus 2pt  % Space between last line of text and
                                        % top of first footnote.
\floatsep 11pt plus 2pt minus 2pt       % Space between adjacent floats moved
                                        % to top or bottom of text page.
\textfloatsep 18pt plus 2pt minus 4pt   % Space between main text and floats
                                        % at top or bottom of page.
\intextsep 11pt plus 2pt minus 2pt      % Space between in-text figures and
                                        % text.
\@ifundefined{@maxsep}{\newdimen\@maxsep}{}% this is for LaTeX2e
\@maxsep 18pt                           % The maximum of \floatsep,
                                        % \textfloatsep and \intextsep (minus
                                        % the stretch and shrink).
\dblfloatsep 11pt plus 2pt minus 2pt    % Same as \floatsep for double-column
                                        % figures in two-column mode.
\dbltextfloatsep 18pt plus 2pt minus 4pt% \textfloatsep for double-column
                                        % floats.
\@ifundefined{@dblmaxsep}{\newdimen\@dblmaxsep}{}% this is for LaTeX2e
\@dblmaxsep 18pt                        % The maximum of \dblfloatsep and
                                        % \dbltexfloatsep.
\@fptop 0pt plus 1fil    % Stretch at top of float page/column. (Must be
                         % 0pt plus ...)
\@fpsep 8pt plus 2fil    % Space between floats on float page/column.
\@fpbot 0pt plus 1fil    % Stretch at bottom of float page/column. (Must be
                         % 0pt plus ... )
\@dblfptop 0pt plus 1fil % Stretch at top of float page. (Must be 0pt plus ...)
\@dblfpsep 8pt plus 2fil % Space between floats on float page.
\@dblfpbot 0pt plus 1fil % Stretch at bottom of float page. (Must be
                         % 0pt plus ... )
\marginparpush 5pt       % Minimum vertical separation between two marginal
                         % notes.

\parskip 0pt plus 1pt            % Extra vertical space between paragraphs.
\parindent 9pt  % GM July 2000 / was 0pt - width of paragraph indentation.
\partopsep 2pt plus 1pt minus 1pt% Extra vertical space, in addition to
                                 % \parskip and \topsep, added when user
                                 % leaves blank line before environment.

\@lowpenalty   51       % Produced by \nopagebreak[1] or \nolinebreak[1]
\@medpenalty  151       % Produced by \nopagebreak[2] or \nolinebreak[2]
\@highpenalty 301       % Produced by \nopagebreak[3] or \nolinebreak[3]

\@beginparpenalty -\@lowpenalty % Before a list or paragraph environment.
\@endparpenalty   -\@lowpenalty % After a list or paragraph environment.
\@itempenalty     -\@lowpenalty % Between list items.

% Try to prevent widow lines.
\clubpenalty=9996
\widowpenalty=9999
\brokenpenalty=4991
\predisplaypenalty=10000
\postdisplaypenalty=1549
\displaywidowpenalty=1602

\@namedef{ds@10pt}{\@latexerr{The `10pt' option is not allowed in the `acmconf'
  document style.}\@eha}
\@namedef{ds@11pt}{\@latexerr{The `11pt' option is not allowed in the `acmconf'
  document style.}\@eha}
\@namedef{ds@12pt}{\@latexerr{The `12pt' option is not allowed in the `acmconf'
  document style.}\@eha}

\@options

\lineskip 2pt           % \lineskip is 1pt for all font sizes.
\normallineskip 2pt
\def\baselinestretch{1}

\abovedisplayskip 9pt plus2pt minus4.5pt%
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip  \z@ plus3pt%
\belowdisplayshortskip  5.4pt plus3pt minus3pt%
\let\@listi\@listI     % Setting of \@listi added 9 Jun 87

\def\small{\@setsize\small{9pt}\viiipt\@viiipt
\abovedisplayskip 7.6pt plus 3pt minus 4pt%
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus2pt%
\belowdisplayshortskip 3.6pt plus2pt minus 2pt
\def\@listi{\leftmargin\leftmargini %% Added 22 Dec 87
\topsep 4pt plus 2pt minus 2pt\parsep 2pt plus 1pt minus 1pt
\itemsep \parsep}}

\def\footnotesize{\@setsize\footnotesize{9pt}\ixpt\@ixpt
\abovedisplayskip 6.4pt plus 2pt minus 4pt%
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus 1pt%
\belowdisplayshortskip 2.7pt plus 1pt minus 2pt
\def\@listi{\leftmargin\leftmargini %% Added 22 Dec 87
\topsep 3pt plus 1pt minus 1pt\parsep 2pt plus 1pt minus 1pt
\itemsep \parsep}}

\newcount\aucount
\newcount\originalaucount
\newdimen\auwidth
\auwidth=\textwidth
\newdimen\auskip
\newcount\auskipcount
\newdimen\auskip
\global\auskip=1pc
\newdimen\allauboxes
\allauboxes=\auwidth
\newtoks\addauthors
\newcount\addauflag
\global\addauflag=0 %Haven't shown additional authors yet

\newtoks\subtitletext
\gdef\subtitle#1{\subtitletext={#1}}

\gdef\additionalauthors#1{\addauthors={#1}}

\gdef\numberofauthors#1{\global\aucount=#1
\ifnum\aucount>3\global\originalaucount=\aucount \global\aucount=3\fi %g}
\global\auskipcount=\aucount\global\advance\auskipcount by 1
\global\multiply\auskipcount by 2
\global\multiply\auskip by \auskipcount
\global\advance\auwidth by -\auskip
\global\divide\auwidth by \aucount}

% \and was modified to count the number of authors.  GKMT 12 Aug 1999
\def\alignauthor{%                  % \begin{tabular}
\end{tabular}%
  \begin{tabular}[t]{p{\auwidth}}\centering}%

%  *** NOTE *** NOTE *** NOTE *** NOTE ***
%  If you have 'font problems' then you may need
%  to change these, e.g. 'arialb' instead of "arialbd".
%  Gerry Murray 11/11/1999
%  *** OR ** comment out block A and activate block B or vice versa.
% **********************************************
%
%  -- Start of block A -- (Type 1 or Truetype fonts)
%\newfont{\secfnt}{timesbd at 12pt} % was timenrb originally - now is timesbd
%\newfont{\secit}{timesbi at 12pt}   %13 Jan 00 gkmt
%\newfont{\subsecfnt}{timesi at 11pt} % was timenrri originally - now is timesi
%\newfont{\subsecit}{timesbi at 11pt} % 13 Jan 00 gkmt -- was times changed to timesbi gm 2/4/2000
%                         % because "normal" is italic, "italic" is Roman
%\newfont{\ttlfnt}{arialbd at 18pt} % was arialb originally - now is arialbd
%\newfont{\ttlit}{arialbi at 18pt}    % 13 Jan 00 gkmt
%\newfont{\subttlfnt}{arial at 14pt} % was arialr originally - now is arial
%\newfont{\subttlit}{ariali at 14pt} % 13 Jan 00 gkmt
%\newfont{\subttlbf}{arialbd at 14pt}  % 13 Jan 00 gkmt
%\newfont{\aufnt}{arial at 12pt} % was arialr originally - now is arial
%\newfont{\auit}{ariali at 12pt} % 13 Jan 00 gkmt
%\newfont{\affaddr}{arial at 10pt} % was arialr originally - now is arial
%\newfont{\affaddrit}{ariali at 10pt} %13 Jan 00 gkmt
%\newfont{\eaddfnt}{arial at 12pt} % was arialr originally - now is arial
%\newfont{\ixpt}{times at 9pt} % was timenrr originally - now is times
%\newfont{\confname}{timesi at 8pt} % was timenrri - now is timesi
%\newfont{\crnotice}{times at 8pt} % was timenrr originally - now is times
%\newfont{\ninept}{times at 9pt} % was timenrr originally - now is times

% *********************************************
%  -- End of block A --
%
%
% -- Start of block B -- METAFONT
% +++++++++++++++++++++++++++++++++++++++++++++
% Next (default) block for those using Metafont
% Gerry Murray 11/11/1999
% *** THIS BLOCK FOR THOSE USING METAFONT *****
% *********************************************
\newfont{\secfnt}{ptmb at 12pt}
\newfont{\secit}{ptmbi at 12pt}    %13 Jan 00 gkmt
\newfont{\subsecfnt}{ptmri at 11pt}
\newfont{\subsecit}{ptmbi at 11pt}  % 13 Jan 00 gkmt -- was ptmr changed to ptmbi gm 2/4/2000
                         % because "normal" is italic, "italic" is Roman
\newfont{\ttlfnt}{phvb at 18pt}
\newfont{\ttlit}{phvbo at 18pt}    % GM 2/4/2000
\newfont{\subttlfnt}{phvr at 14pt}
\newfont{\subttlit}{phvro at 14pt} % GM 2/4/2000
\newfont{\subttlbf}{phvb at 14pt}  % 13 Jan 00 gkmt
\newfont{\aufnt}{phvr at 12pt}
\newfont{\auit}{phvro at 12pt}     % GM 2/4/2000
\newfont{\affaddr}{phvr at 10pt}
\newfont{\affaddrit}{phvro at 10pt} % GM 2/4/2000
\newfont{\eaddfnt}{phvr at 12pt}
\newfont{\ixpt}{ptmr at 9pt}
\newfont{\confname}{ptmri at 8pt}
\newfont{\crnotice}{ptmr at 8pt}
\newfont{\ninept}{ptmr at 9pt}
% +++++++++++++++++++++++++++++++++++++++++++++
% -- End of block B --


\def\email#1{{{\eaddfnt{\vskip 4pt#1}}}}

\def\addauthorsection{\ifnum\originalaucount>3
    \section{Additional Authors}\the\addauthors
  \fi}

\newcount\savesection
\newcount\sectioncntr
\global\sectioncntr=1

\setcounter{secnumdepth}{3}

\def\appendix{\par
\section*{APPENDIX}
\setcounter{section}{0}
 \setcounter{subsection}{0}
 \def\thesection{\Alph{section}} }

\leftmargini 22.5pt
\leftmarginii 19.8pt    % > \labelsep + width of '(m)'
\leftmarginiii 16.8pt   % > \labelsep + width of 'vii.'
\leftmarginiv 15.3pt    % > \labelsep + width of 'M.'
\leftmarginv 9pt
\leftmarginvi 9pt

\leftmargin\leftmargini
\labelsep 4.5pt
\labelwidth\leftmargini\advance\labelwidth-\labelsep

\def\@listI{\leftmargin\leftmargini \parsep 3.6pt plus 2pt minus 1pt%
\topsep 7.2pt plus 2pt minus 4pt%
\itemsep 3.6pt plus 2pt minus 1pt}

\let\@listi\@listI
\@listi

\def\@listii{\leftmargin\leftmarginii
   \labelwidth\leftmarginii\advance\labelwidth-\labelsep
   \topsep 3.6pt plus 2pt minus 1pt
   \parsep 1.8pt plus 0.9pt minus 0.9pt
   \itemsep \parsep}

\def\@listiii{\leftmargin\leftmarginiii
    \labelwidth\leftmarginiii\advance\labelwidth-\labelsep
    \topsep 1.8pt plus 0.9pt minus 0.9pt
    \parsep \z@ \partopsep 1pt plus 0pt minus 1pt
    \itemsep \topsep}

\def\@listiv{\leftmargin\leftmarginiv
     \labelwidth\leftmarginiv\advance\labelwidth-\labelsep}

\def\@listv{\leftmargin\leftmarginv
     \labelwidth\leftmarginv\advance\labelwidth-\labelsep}

\def\@listvi{\leftmargin\leftmarginvi
     \labelwidth\leftmarginvi\advance\labelwidth-\labelsep}

\def\labelenumi{\theenumi.}
\def\theenumi{\arabic{enumi}}

\def\labelenumii{(\theenumii)}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}

\def\labelenumiii{\theenumiii.}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}

\def\labelenumiv{\theenumiv.}
\def\theenumiv{\Alph{enumiv}}
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{$\bullet$}
\def\labelitemii{\bf --}
\def\labelitemiii{$\ast$}
\def\labelitemiv{$\cdot$}

\def\verse{\let\\=\@centercr
  \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent
          \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist

\def\quotation{\list{}{\listparindent 1.5em
    \itemindent\listparindent
    \rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]}
\let\endquotation=\endlist

\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
       \let\makelabel\descriptionlabel}}

\let\enddescription\endlist

\def\theequation{\arabic{equation}}

\arraycolsep 4.5pt   % Half the space between columns in an array environment.
\tabcolsep 5.4pt    % Half the space between columns in a tabular environment.
\arrayrulewidth .4pt % Width of rules in array and tabular environment.
\doublerulesep 1.8pt % Space between adjacent rules in array or tabular env.

\tabbingsep \labelsep   % Space used by the \' command.  (See LaTeX manual.)

\skip\@mpfootins =\skip\footins

\fboxsep =2.7pt      % Space left between box and text by \fbox and \framebox.
\fboxrule =.4pt      % Width of rules in box made by \fbox and \framebox.

\def\thepart{\Roman{part}} % Roman numeral part numbers.
\def\thesection       {\arabic{section}}
\def\thesubsection    {\thesection.\arabic{subsection}}
%\def\thesubsubsection {\thesubsection.\arabic{subsubsection}} % GM 7/30/2002
%\def\theparagraph     {\thesubsubsection.\arabic{paragraph}}  % GM 7/30/2002
\def\thesubparagraph  {\theparagraph.\arabic{subparagraph}}

\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}

\def\tableofcontents{\@latexerr{\tableofcontents: Tables of contents are not
  allowed in the `acmconf' document style.}\@eha}

\def\l@part#1#2{\addpenalty{\@secpenalty}
   \addvspace{2.25em plus 1pt}  % space above part line
   \begingroup
   \@tempdima 3em       % width of box holding part number, used by
     \parindent \z@ \rightskip \@pnumwidth      %% \numberline
     \parfillskip -\@pnumwidth
     {\large \bf        % set line in \large boldface
     \leavevmode        % TeX command to enter horizontal mode.
     #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
     \nobreak           % Never break after part entry
   \endgroup}

\def\l@section#1#2{\addpenalty{\@secpenalty} % good place for page break
   \addvspace{1.0em plus 1pt}   % space above toc entry
   \@tempdima 1.5em             % width of box holding section number
   \begingroup
    \parindent  \z@ \rightskip \@pnumwidth
     \parfillskip -\@pnumwidth
     \bf                        % Boldface.
     \leavevmode                % TeX command to enter horizontal mode.
      \advance\leftskip\@tempdima %% added 5 Feb 88 to conform to
      \hskip -\leftskip           %% 25 Jan 88 change to \numberline
     #1\nobreak\hfil \nobreak\hbox to\@pnumwidth{\hss #2}\par
   \endgroup}


\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}

\def\listoffigures{\@latexerr{\listoffigures: Lists of figures are not
  allowed in the `acmconf' document style.}\@eha}

\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}

\def\listoftables{\@latexerr{\listoftables: Lists of tables are not
  allowed in the `acmconf' document style.}\@eha}
\let\l@table\l@figure

\def\footnoterule{\kern-3\p@
  \hrule width .4\columnwidth
  \kern 2.6\p@}                 % The \hrule has default height of .4pt .
% ------
\long\def\@makefntext#1{\noindent 
%\hbox to .5em{\hss$^{\@thefnmark}$}#1}   % original
%\hbox to .5em{\hss\textsuperscript{\@thefnmark}}#1}  % new original b4 FJ edit
\hbox to .0em{\hss\textsuperscript{\@thefnmark}}#1}  % FJ edit
% -------

\long\def\@maketntext#1{\noindent
#1}

\long\def\@maketitlenotetext#1#2{\noindent
            \hbox to 1.8em{\hss$^{#1}$}#2}

\setcounter{topnumber}{2}
\def\topfraction{.7}
\setcounter{bottomnumber}{1}
\def\bottomfraction{.3}
\setcounter{totalnumber}{3}
\def\textfraction{.2}
\def\floatpagefraction{.5}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.7}
\def\dblfloatpagefraction{.5}

%
\long\def\@makecaption#1#2{
   \vskip \baselineskip
   \setbox\@tempboxa\hbox{\textbf{#1: #2}}
   \ifdim \wd\@tempboxa >\hsize % IF longer than one line:
       \textbf{#1: #2}\par               %   THEN set as ordinary paragraph.
     \else                      %   ELSE  center.
       \hbox to\hsize{\hfil\box\@tempboxa\hfil}\par
   \fi}

%

\long\def\@makecaption#1#2{
   \vskip 10pt
   \setbox\@tempboxa\hbox{\textbf{#1: #2}}
   \ifdim \wd\@tempboxa >\hsize % IF longer than one line:
       \textbf{#1: #2}\par                %   THEN set as ordinary paragraph.
     \else                      %   ELSE  center.
       \hbox to\hsize{\hfil\box\@tempboxa\hfil}
   \fi}

\@ifundefined{figure}{\newcounter {figure}} % this is for LaTeX2e

\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{Figure \thefigure}
\def\figure{\@float{figure}}
\let\endfigure\end@float
\@namedef{figure*}{\@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}

\@ifundefined{table}{\newcounter {table}} % this is for LaTeX2e

\def\fps@table{tbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{Table \thetable}
\def\table{\@float{table}}
\let\endtable\end@float
\@namedef{table*}{\@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}

\newtoks\titleboxnotes
\newcount\titleboxnoteflag

\def\maketitle{\par
 \begingroup
   \def\thefootnote{\fnsymbol{footnote}}
   \def\@makefnmark{\hbox
       to 0pt{$^{\@thefnmark}$\hss}}
     \twocolumn[\@maketitle]
\@thanks
 \endgroup
 \setcounter{footnote}{0}
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\gdef\@subtitle{}\let\thanks\relax
% \@copyrightspace
}

%% CHANGES ON NEXT LINES
\newif\if@ll % to record which version of LaTeX is in use

\expandafter\ifx\csname LaTeXe\endcsname\relax % LaTeX2.09 is used
\else% LaTeX2e is used, so set ll to true
\global\@lltrue
\fi

\if@ll
  \NeedsTeXFormat{LaTeX2e}
  \ProvidesClass{vldb} [2010/10/19 - V1.8b - based on sig-alternate V1.8 - based on acmproc.cls V1.3 <Nov. 30 '99>]
  \RequirePackage{latexsym}% QUERY: are these two really needed?
  \let\dooptions\ProcessOptions
\else
  \let\dooptions\@options
\fi
%% END CHANGES

\def\@height{height}
\def\@width{width}
\def\@minus{minus}
\def\@plus{plus}
\def\hb@xt@{\hbox to}
\newif\if@faircopy
\@faircopyfalse
\def\ds@faircopy{\@faircopytrue}

\def\ds@preprint{\@faircopyfalse}

\@twosidetrue
\@mparswitchtrue
\def\ds@draft{\overfullrule 5\p@}
%% CHANGE ON NEXT LINE
\dooptions

\lineskip \p@
\normallineskip \p@
\def\baselinestretch{1}
\def\@ptsize{0} %needed for amssymbols.sty

%% CHANGES ON NEXT LINES
\if@ll% allow use of old-style font change commands in LaTeX2e
\@maxdepth\maxdepth
%
\DeclareOldFontCommand{\rm}{\ninept\rmfamily}{\mathrm}
\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
\DeclareRobustCommand*{\cal}{\@fontswitch{\relax}{\mathcal}}
\DeclareRobustCommand*{\mit}{\@fontswitch{\relax}{\mathnormal}}
\fi
%
\if@ll
 \renewcommand{\rmdefault}{cmr}  % was 'ttm'
% Note! I have also found 'mvr' to work ESPECIALLY well.
% Gerry - October 1999
% You may need to change your LV1times.fd file so that sc is
% mapped to cmcsc - -for smallcaps -- that is if you decide
% to change {cmr} to {times} above. (Not recommended)
  \renewcommand{\@ptsize}{}
  \renewcommand{\normalsize}{%
    \@setfontsize\normalsize\@ixpt{10.5\p@}%\ninept%
    \abovedisplayskip 6\p@ \@plus2\p@ \@minus\p@
    \belowdisplayskip \abovedisplayskip
    \abovedisplayshortskip 6\p@ \@minus 3\p@
    \belowdisplayshortskip 6\p@ \@minus 3\p@
    \let\@listi\@listI
  }
\else
  \def\@normalsize{%changed next to 9 from 10
    \@setsize\normalsize{9\p@}\ixpt\@ixpt
   \abovedisplayskip 6\p@ \@plus2\p@ \@minus\p@
    \belowdisplayskip \abovedisplayskip
    \abovedisplayshortskip 6\p@ \@minus 3\p@
    \belowdisplayshortskip 6\p@ \@minus 3\p@
    \let\@listi\@listI
  }%
\fi
\if@ll
  \newcommand\scriptsize{\@setfontsize\scriptsize\@viipt{8\p@}}
  \newcommand\tiny{\@setfontsize\tiny\@vpt{6\p@}}
  \newcommand\large{\@setfontsize\large\@xiipt{14\p@}}
  \newcommand\Large{\@setfontsize\Large\@xivpt{18\p@}}
  \newcommand\LARGE{\@setfontsize\LARGE\@xviipt{20\p@}}
  \newcommand\huge{\@setfontsize\huge\@xxpt{25\p@}}
  \newcommand\Huge{\@setfontsize\Huge\@xxvpt{30\p@}}
\else
  \def\scriptsize{\@setsize\scriptsize{8\p@}\viipt\@viipt}
  \def\tiny{\@setsize\tiny{6\p@}\vpt\@vpt}
  \def\large{\@setsize\large{14\p@}\xiipt\@xiipt}
  \def\Large{\@setsize\Large{18\p@}\xivpt\@xivpt}
  \def\LARGE{\@setsize\LARGE{20\p@}\xviipt\@xviipt}
  \def\huge{\@setsize\huge{25\p@}\xxpt\@xxpt}
  \def\Huge{\@setsize\Huge{30\p@}\xxvpt\@xxvpt}
\fi
\normalsize

% make aubox hsize/number of authors up to 3, less gutter
% then showbox gutter showbox gutter showbox -- GKMT Aug 99
\newbox\@acmtitlebox
\def\@maketitle{\newpage
 \null
 \setbox\@acmtitlebox\vbox{%
\baselineskip 20pt
\vskip 2em                   % Vertical space above title.
   \begin{center}
    {\ttlfnt \@title\par}       % Title set in 18pt Helvetica (Arial) bold size.
    \vskip 1.5em                % Vertical space after title.
%This should be the subtitle.
{\subttlfnt \the\subtitletext\par}\vskip 1.25em%\fi
    {\baselineskip 16pt\aufnt   % each author set in \12 pt Arial, in a
     \lineskip .5em             % tabular environment
     \begin{tabular}[t]{c}\@author
     \end{tabular}\par}
    \vskip 1.5em               % Vertical space after author.
   \end{center}}
 \dimen0=\ht\@acmtitlebox
 \advance\dimen0 by -6.75pc\relax % Increased space for title box -- KBT
 \unvbox\@acmtitlebox
 \ifdim\dimen0<0.0pt\relax\vskip-\dimen0\fi}


\newcount\titlenotecount
\global\titlenotecount=0
\newtoks\tntoks
\newtoks\tntokstwo
\newtoks\tntoksthree
\newtoks\tntoksfour
\newtoks\tntoksfive

\def\abstract{
\ifnum\titlenotecount>0 % was =1
    \insert\footins{%
    \reset@font\footnotesize
        \interlinepenalty\interfootnotelinepenalty
        \splittopskip\footnotesep
        \splitmaxdepth \dp\strutbox \floatingpenalty \@MM
        \hsize\columnwidth \@parboxrestore
        \protected@edef\@currentlabel{%
        }%
        \color@begingroup
\ifnum\titlenotecount=1
      \@maketntext{%
         \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\@finalstrut\strutbox}%
\fi
\ifnum\titlenotecount=2
      \@maketntext{%
      \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\dagger$}\rule\z@\footnotesep\ignorespaces\the\tntokstwo\@finalstrut\strutbox}%
\fi
\ifnum\titlenotecount=3
      \@maketntext{%
         \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\dagger$}\rule\z@\footnotesep\ignorespaces\the\tntokstwo\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\ddagger$}\rule\z@\footnotesep\ignorespaces\the\tntoksthree\@finalstrut\strutbox}%
\fi
\ifnum\titlenotecount=4
      \@maketntext{%
         \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\dagger$}\rule\z@\footnotesep\ignorespaces\the\tntokstwo\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\ddagger$}\rule\z@\footnotesep\ignorespaces\the\tntoksthree\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\S$}\rule\z@\footnotesep\ignorespaces\the\tntoksfour\@finalstrut\strutbox}%
\fi
\ifnum\titlenotecount=5
      \@maketntext{%
         \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\dagger$}\rule\z@\footnotesep\ignorespaces\the\tntokstwo\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\ddagger$}\rule\z@\footnotesep\ignorespaces\the\tntoksthree\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\S$}\rule\z@\footnotesep\ignorespaces\the\tntoksfour\par\@finalstrut\strutbox}%
\@maketntext{%
         \raisebox{4pt}{$\P$}\rule\z@\footnotesep\ignorespaces\the\tntoksfive\@finalstrut\strutbox}%
\fi
   \color@endgroup} %g}
\fi
\setcounter{footnote}{0}
\section*{ABSTRACT}\normalsize%\ninept
}

\def\endabstract{\if@twocolumn\else\endquotation\fi}

\def\keywords{\if@twocolumn
\section*{Keywords}
\else \small
\quotation
\fi}

\def\terms{\if@twocolumn
\section*{General Terms}
\else \small
\quotation
\fi}

% -- Classification needs to be a bit smart due to optionals - Gerry/Georgia November 2nd. 1999
\newcount\catcount
\global\catcount=1

\def\category#1#2#3{%
\ifnum\catcount=1
\section*{Categories and Subject Descriptors}
\advance\catcount by 1\else{\unskip; }\fi
    \@ifnextchar [{\@category{#1}{#2}{#3}}{\@category{#1}{#2}{#3}[]}%
}

\def\@category#1#2#3[#4]{%
    \begingroup
        \let\and\relax
            #1 [\textbf{#2}]%
            \if!#4!%
                \if!#3!\else : #3\fi
            \else
                :\space
                \if!#3!\else #3\kern\z@---\hskip\z@\fi
                \textit{#4}%
            \fi
    \endgroup
}
%

%%% This section (written by KBT) handles the 1" box in the lower left
%%% corner of the left column of the first page by creating a picture,
%%% and inserting the predefined string at the bottom (with a negative
%%% displacement to offset the space allocated for a non-existent
%%% caption).
%%%
\newtoks\copyrightnotice
\def\ftype@copyrightbox{8}
\def\@copyrightspace{
\@float{copyrightbox}[b]
\begin{center}
\setlength{\unitlength}{1pc}
\begin{picture}(20,6) %Space for copyright notice
\put(0,-0.95){\crnotice{\@toappear}}
\end{picture}
\end{center}
\end@float}

\def\@toappear{} % Default setting blank - commands below change this.
\long\def\toappear#1{\def\@toappear{\parbox[b]{20pc}{\baselineskip 9pt#1}}}
\def\toappearbox#1{\def\@toappear{\raisebox{5pt}{\framebox[20pc]{\parbox[b]{19pc}{#1}}}}}

\newtoks\conf
\newtoks\confinfo
\def\conferenceinfo#1#2{\global\conf={#1}\global\confinfo{#2}}


\def\marginpar{\@latexerr{The \marginpar command is not allowed in the
  `acmconf' document style.}\@eha}

\mark{{}{}}     % Initializes TeX's marks

\def\today{\ifcase\month\or
  January\or February\or March\or April\or May\or June\or
  July\or August\or September\or October\or November\or December\fi
  \space\number\day, \number\year}

\def\@begintheorem#1#2{%
    \parskip 0pt % GM July 2000 (for tighter spacing)
    \trivlist
    \item[%
        \hskip 10\p@
        \hskip \labelsep
        {{\sc #1}\hskip 5\p@\relax#2.}%
    ]
    \it
}
\def\@opargbegintheorem#1#2#3{%
    \parskip 0pt % GM July 2000 (for tighter spacing)
    \trivlist
    \item[%
        \hskip 10\p@
        \hskip \labelsep
        {\sc #1\ #2\             % This mod by Gerry to enumerate corollaries
   \setbox\@tempboxa\hbox{(#3)}  % and bracket the 'corollary title'
        \ifdim \wd\@tempboxa>\z@ % and retain the correct numbering of e.g. theorems
            \hskip 5\p@\relax    % if they occur 'around' said corollaries.
            \box\@tempboxa       % Gerry - Nov. 1999.
        \fi.}%
    ]
    \it
}
\newif\if@qeded
\global\@qededfalse

% -- original
%\def\proof{%
%  \vspace{-\parskip} % GM July 2000 (for tighter spacing)
%    \global\@qededfalse
%    \@ifnextchar[{\@xproof}{\@proof}%
%}
% -- end of original

% (JSS) Fix for vertical spacing bug - Gerry Murray July 30th. 2002
\def\proof{%
\vspace{-\lastskip}\vspace{-\parsep}\penalty-51%
\global\@qededfalse
\@ifnextchar[{\@xproof}{\@proof}%
}

\def\endproof{%
    \if@qeded\else\qed\fi
    \endtrivlist
}
\def\@proof{%
    \trivlist
    \item[%
        \hskip 10\p@
        \hskip \labelsep
        {\sc Proof.}%
    ]
    \ignorespaces
}
\def\@xproof[#1]{%
    \trivlist
    \item[\hskip 10\p@\hskip \labelsep{\sc Proof #1.}]%
    \ignorespaces
}
\def\qed{%
    \unskip
    \kern 10\p@
    \begingroup
        \unitlength\p@
        \linethickness{.4\p@}%
        \framebox(6,6){}%
    \endgroup
    \global\@qededtrue
}

\def\newdef#1#2{%
    \expandafter\@ifdefinable\csname #1\endcsname
        {\@definecounter{#1}%
         \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
         \global\@namedef{#1}{\@defthm{#1}{#2}}%
         \global\@namedef{end#1}{\@endtheorem}%
    }%
}
\def\@defthm#1#2{%
    \refstepcounter{#1}%
    \@ifnextchar[{\@ydefthm{#1}{#2}}{\@xdefthm{#1}{#2}}%
}
\def\@xdefthm#1#2{%
    \@begindef{#2}{\csname the#1\endcsname}%
    \ignorespaces
}
\def\@ydefthm#1#2[#3]{%
    \trivlist
    \item[%
        \hskip 10\p@
        \hskip \labelsep
        {\it #2%
         \savebox\@tempboxa{#3}%
         \ifdim \wd\@tempboxa>\z@
            \ \box\@tempboxa
         \fi.%
        }]%
    \ignorespaces
}
\def\@begindef#1#2{%
    \trivlist
    \item[%
        \hskip 10\p@
        \hskip \labelsep
        {\it #1\ \rm #2.}%
    ]%
}
\def\theequation{\arabic{equation}}

\newcounter{part}
\newcounter{section}
\newcounter{subsection}[section]
\newcounter{subsubsection}[subsection]
\newcounter{paragraph}[subsubsection]
\def\thepart{\Roman{part}}
\def\thesection{\arabic{section}}
\def\thesubsection{\thesection.\arabic{subsection}}
\def\thesubsubsection{\thesubsection.\arabic{subsubsection}} %removed \subsecfnt 29 July 2002 gkmt
\def\theparagraph{\thesubsubsection.\arabic{paragraph}} %removed \subsecfnt 29 July 2002 gkmt
\newif\if@uchead
\@ucheadfalse

%% CHANGES: NEW NOTE
%% NOTE: OK to use old-style font commands below, since they were
%% suitably redefined for LaTeX2e
%% END CHANGES
\setcounter{secnumdepth}{3}
\def\part{%
    \@startsection{part}{9}{\z@}{-10\p@ \@plus -4\p@ \@minus -2\p@}
        {4\p@}{\normalsize\@ucheadtrue}%
}
\def\section{%
    \@startsection{section}{1}{\z@}{-10\p@ \@plus -4\p@ \@minus -2\p@}% GM
    {4\p@}{\baselineskip 14pt\secfnt\@ucheadtrue}%
}

\def\subsection{%
    \@startsection{subsection}{2}{\z@}{-8\p@ \@plus -2\p@ \@minus -\p@}
    {4\p@}{\secfnt}%
}
\def\subsubsection{%
    \@startsection{subsubsection}{3}{\z@}{-8\p@ \@plus -2\p@ \@minus -\p@}%
    {4\p@}{\subsecfnt}%
}
\def\paragraph{%
    \vskip 12pt\@startsection{paragraph}{3}{\z@}{6\p@ \@plus \p@}%
    {-5\p@}{\subsecfnt}%
}
\let\@period=.
\def\@startsection#1#2#3#4#5#6{%
        \if@noskipsec  %gkmt, 11 aug 99
        \global\let\@period\@empty
        \leavevmode
        \global\let\@period.%
    \fi
      \par %
    \@tempskipa #4\relax
    \@afterindenttrue
    \ifdim \@tempskipa <\z@
        \@tempskipa -\@tempskipa
        \@afterindentfalse
    \fi
    \if@nobreak
    \everypar{}%
    \else
        \addpenalty\@secpenalty
        \addvspace\@tempskipa
    \fi
\parskip=0pt % GM July 2000 (non numbered) section heads
    \@ifstar
        {\@ssect{#3}{#4}{#5}{#6}}
        {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}%
}
\def\@sect#1#2#3#4#5#6[#7]#8{%
    \ifnum #2>\c@secnumdepth
        \let\@svsec\@empty
    \else
        \refstepcounter{#1}%
        \edef\@svsec{%
            \begingroup
                %\ifnum#2>2 \noexpand\rm \fi % changed to next 29 July 2002 gkmt
                        \ifnum#2>2 \noexpand#6 \fi
                \csname the#1\endcsname
            \endgroup
            \ifnum #2=1\relax .\fi
            \hskip 1em
        }%
    \fi
    \@tempskipa #5\relax
    \ifdim \@tempskipa>\z@
        \begingroup
            #6\relax
            \@hangfrom{\hskip #3\relax\@svsec}%
            \begingroup
                \interlinepenalty \@M
                \if@uchead
                    \uppercase{#8}%
                \else
                    #8%
                \fi
                \par
            \endgroup
        \endgroup
        \csname #1mark\endcsname{#7}%
        \vskip -12pt  %gkmt, 11 aug 99 and GM July 2000 (was -14) - numbered section head spacing
\addcontentsline{toc}{#1}{%
            \ifnum #2>\c@secnumdepth \else
                \protect\numberline{\csname the#1\endcsname}%
            \fi
            #7%
        }%
    \else
        \def\@svsechd{%
            #6%
            \hskip #3\relax
            \@svsec
            \if@uchead
                \uppercase{#8}%
            \else
                #8%
            \fi
            \csname #1mark\endcsname{#7}%
            \addcontentsline{toc}{#1}{%
                \ifnum #2>\c@secnumdepth \else
                    \protect\numberline{\csname the#1\endcsname}%
                \fi
                #7%
            }%
        }%
    \fi
    \@xsect{#5}\hskip 1pt
    \par
}
\def\@xsect#1{%
    \@tempskipa #1\relax
    \ifdim \@tempskipa>\z@
        \par
        \nobreak
        \vskip \@tempskipa
        \@afterheading
    \else
        \global\@nobreakfalse
        \global\@noskipsectrue
        \everypar{%
            \if@noskipsec
                \global\@noskipsecfalse
                \clubpenalty\@M
                \hskip -\parindent
                \begingroup
                    \@svsechd
                    \@period
                \endgroup
                \unskip
                \@tempskipa #1\relax
                \hskip -\@tempskipa
            \else
                \clubpenalty \@clubpenalty
                \everypar{}%
            \fi
        }%
    \fi
    \ignorespaces
}
\def\@trivlist{%
    \@topsepadd\topsep
    \if@noskipsec
        \global\let\@period\@empty
        \leavevmode
        \global\let\@period.%
    \fi
    \ifvmode
        \advance\@topsepadd\partopsep
    \else
        \unskip
        \par
    \fi
    \if@inlabel
        \@noparitemtrue
        \@noparlisttrue
    \else
        \@noparlistfalse
        \@topsep\@topsepadd
    \fi
    \advance\@topsep \parskip
    \leftskip\z@skip
    \rightskip\@rightskip
    \parfillskip\@flushglue
    \@setpar{\if@newlist\else{\@@par}\fi}
    \global\@newlisttrue
    \@outerparskip\parskip
}

%%% Actually, 'abbrev' works just fine as the default
%%% Bibliography style.

\typeout{Using 'Abbrev' bibliography style}
\newcommand\bibyear[2]{%
    \unskip\quad\ignorespaces#1\unskip
    \if#2..\quad \else \quad#2 \fi
}
\newcommand{\bibemph}[1]{{\em#1}}
\newcommand{\bibemphic}[1]{{\em#1\/}}
\newcommand{\bibsc}[1]{{\sc#1}}
\def\@normalcite{%
    \def\@cite##1##2{[##1\if@tempswa , ##2\fi]}%
}
\def\@citeNB{%
    \def\@cite##1##2{##1\if@tempswa , ##2\fi}%
}
\def\@citeRB{%
    \def\@cite##1##2{##1\if@tempswa , ##2\fi]}%
}
\def\start@cite#1#2{%
    \edef\citeauthoryear##1##2##3{%
        ###1%
        \ifnum#2=\z@ \else\ ###2\fi
    }%
    \ifnum#1=\thr@@
        \let\@@cite\@citeyear
    \else
        \let\@@cite\@citenormal
    \fi
    \@ifstar{\@citeNB\@@cite}{\@normalcite\@@cite}%
}
\def\cite{\start@cite23}
\def\citeNP{\cite*}
\def\citeA{\start@cite10}
\def\citeANP{\citeA*}
\def\shortcite{\start@cite23}
\def\shortciteNP{\shortcite*}
\def\shortciteA{\start@cite20}
\def\shortciteANP{\shortciteA*}
\def\citeyear{\start@cite30}
\def\citeyearNP{\citeyear*}
\def\citeN{%
    \@citeRB
    \def\citeauthoryear##1##2##3{##1\ [##3%
        \def\reserved@a{##1}%
        \def\citeauthoryear####1####2####3{%
            \def\reserved@b{####1}%
            \ifx\reserved@a\reserved@b
                ####3%
            \else
                \errmessage{Package acmart Error: author mismatch
                         in \string\citeN^^J^^J%
                    See the acmart package documentation for explanation}%
            \fi
        }%
    }%
    \@ifstar\@citeyear\@citeyear
}
\def\shortciteN{%
    \@citeRB
    \def\citeauthoryear##1##2##3{##2\ [##3%
        \def\reserved@a{##2}%
        \def\citeauthoryear####1####2####3{%
            \def\reserved@b{####2}%
            \ifx\reserved@a\reserved@b
                ####3%
            \else
                \errmessage{Package acmart Error: author mismatch
                         in \string\shortciteN^^J^^J%
                    See the acmart package documentation for explanation}%
            \fi
        }%
    }%
    \@ifstar\@citeyear\@citeyear  % GM July 2000
}
\def\@citenormal{%
    \@ifnextchar [{\@tempswatrue\@citex;}
                  {\@tempswafalse\@citex,[]}% % GM July 2000
}
\def\@citeyear{%
    \@ifnextchar [{\@tempswatrue\@citex,}%
                  {\@tempswafalse\@citex,[]}%
}
\def\@citex#1[#2]#3{%
    \let\@citea\@empty
    \@cite{%
        \@for\@citeb:=#3\do{%
            \@citea
            \def\@citea{#1 }%
            \edef\@citeb{\expandafter\@iden\@citeb}%
            \if@filesw
                \immediate\write\@auxout{\string\citation{\@citeb}}%
            \fi
            \@ifundefined{b@\@citeb}{%
                {\bf ?}%
                \@warning{%
                    Citation `\@citeb' on page \thepage\space undefined%
                }%
            }%
            {\csname b@\@citeb\endcsname}%
        }%
    }{#2}%
}
\let\@biblabel\@gobble
\newdimen\bibindent
\setcounter{enumi}{1}
\bibindent=0em
\def\thebibliography#1{% 
\ifnum\addauflag=0\addauthorsection\global\addauflag=1\fi
     \section[References]{%    <=== OPTIONAL ARGUMENT ADDED HERE
        {References} % was uppercased but this affects pdf bookmarks (SP/GM October 2004)
          \vskip -9pt  % GM July 2000 (for tighter spacing)
         \@mkboth{{\refname}}{{\refname}}%
     }%
     \list{[\arabic{enumi}]}{%
         \settowidth\labelwidth{[#1]}%
         \leftmargin\labelwidth
         \advance\leftmargin\labelsep
         \advance\leftmargin\bibindent
         \parsep=0pt\itemsep=1pt % GM July 2000
         \itemindent -\bibindent
         \listparindent \itemindent
         \usecounter{enumi}
     }%
     \let\newblock\@empty
     \raggedright % GM July 2000
     \sloppy
     \sfcode`\.=1000\relax
}


\gdef\balancecolumns
{\vfill\eject
\global\@colht=\textheight
\global\ht\@cclv=\textheight
}

\newcount\colcntr
\global\colcntr=0
\newbox\savebox

\gdef \@makecol {%
\global\advance\colcntr by 1
\ifnum\colcntr>2 \global\colcntr=1\fi
   \ifvoid\footins
     \setbox\@outputbox \box\@cclv
   \else
     \setbox\@outputbox \vbox{%
\boxmaxdepth \@maxdepth
       \@tempdima\dp\@cclv
       \unvbox \@cclv
       \vskip-\@tempdima
       \vskip \skip\footins
       \color@begingroup
         \normalcolor
         \footnoterule
         \unvbox \footins
       \color@endgroup
       }%
   \fi
   \xdef\@freelist{\@freelist\@midlist}%
   \global \let \@midlist \@empty
   \@combinefloats
   \ifvbox\@kludgeins
     \@makespecialcolbox
   \else
     \setbox\@outputbox \vbox to\@colht {%
\@texttop
       \dimen@ \dp\@outputbox
       \unvbox \@outputbox
   \vskip -\dimen@
       \@textbottom
       }%
   \fi
   \global \maxdepth \@maxdepth
}
\def\titlenote{\@ifnextchar[\@xtitlenote{\stepcounter\@mpfn
\global\advance\titlenotecount by 1
\ifnum\titlenotecount=1
    \raisebox{9pt}{$\ast$}
\fi
\ifnum\titlenotecount=2
    \raisebox{9pt}{$\dagger$}
\fi
\ifnum\titlenotecount=3
    \raisebox{9pt}{$\ddagger$}
\fi
\ifnum\titlenotecount=4
\raisebox{9pt}{$\S$}
\fi
\ifnum\titlenotecount=5
\raisebox{9pt}{$\P$}
\fi
         \@titlenotetext
}}

\long\def\@titlenotetext#1{\insert\footins{%
\ifnum\titlenotecount=1\global\tntoks={#1}\fi
\ifnum\titlenotecount=2\global\tntokstwo={#1}\fi
\ifnum\titlenotecount=3\global\tntoksthree={#1}\fi
\ifnum\titlenotecount=4\global\tntoksfour={#1}\fi
\ifnum\titlenotecount=5\global\tntoksfive={#1}\fi
    \reset@font\footnotesize
    \interlinepenalty\interfootnotelinepenalty
    \splittopskip\footnotesep
    \splitmaxdepth \dp\strutbox \floatingpenalty \@MM
    \hsize\columnwidth \@parboxrestore
    \protected@edef\@currentlabel{%
    }%
    \color@begingroup
   \color@endgroup}}

%%%%%%%%%%%%%%%%%%%%%%%%%
\ps@plain
\baselineskip=11pt
\let\thepage\relax % For NO page numbers - GM Nov. 30th. 1999 and July 2000
\def\setpagenumber#1{\global\setcounter{page}{#1}}
\pagenumbering{arabic}  % Arabic page numbers GM July 2000
\twocolumn             % Double column.
\flushbottom           % Even bottom -- alas, does not balance columns at end of document
\pagestyle{plain}

% Need Copyright Year and Copyright Data to be user definable (in .tex file).
% Gerry Nov. 30th. 1999
\newtoks\copyrtyr
\newtoks\acmcopyr
\newtoks\boilerplate
\global\acmcopyr={X-XXXXX-XX-X/XX/XX}  % Default - 5/11/2001 *** Gerry
\global\copyrtyr={200X}                % Default - 3/3/2003 *** Gerry
\def\CopyrightYear#1{\global\copyrtyr{#1}}
\def\crdata#1{\global\acmcopyr{#1}}
\def\permission#1{\global\boilerplate{#1}}
%
%\global\boilerplate={Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.  To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.}
%\newtoks\copyrightetc
%\global\copyrightetc{Copyright \the\copyrtyr\ ACM \the\acmcopyr\ ...\$5.00}

\global\boilerplate={Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.  Articles from this volume were invited to present their results at The 38th International Conference on Very Large Data Bases, August 26th - 31st 2013, Riva del Garda, Trento, Italy. }

\global\conf{Proceedings of the VLDB Endowment,}
\global\confinfo{Vol. 6, No. XXX}
\newtoks\copyrightetc
\global\copyrightetc{Copyright 2011 VLDB Endowment 2150-8097/11/11... \$ 10.00}
		
%ahmetsacan, 20111024: disabled showing conference name and Vol/Issue/Month. We now stamp this on the papers ourselves.
%\toappear{\the\boilerplate\par
%{\confname{\the\conf}} \the\confinfo\par \the\copyrightetc.
%}
%
%% End of vldb.cls -- V1.8c - 05/15/2011 --
%% Ahmet Sacan  -- December 2011 (volume, issue, and dates are dynamically updated)
%% Uwe Roehm    -- Oct-Dec 2010 & Jan-Apr 2011
%% Gerry Murray -- Wednesday July 26th. 2005