\oddsidemargin 0in \evensidemargin 0in \marginparwidth 40pt \marginparsep 10pt \topmargin 0pt \headsep 0in \headheight 0in \textheight 8.5in \textwidth 6.5in \brokenpenalty=10000 \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \usepackage{amsthm} \usepackage{latexsym} \usepackage{epsfig} \usepackage{bm} \usepackage{xspace} %\usepackage{times} %\usepackage{hyperref} \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{claim}[theorem]{Claim} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{fact}[theorem]{Fact} \newtheorem{example}[theorem]{Example} \newtheorem{notation}[theorem]{Notation} \newtheorem{observation}[theorem]{Observation} \newtheorem{conjecture}[theorem]{Conjecture} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} % Setting the theorem style back to plain in case theorems are defined in the main file \theoremstyle{plain} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Useful macros %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % for temporarily chunks of text \newcommand{\eat}[1]{} % Probability/expectation operators. The ones ending in x should be used if you want % subscripts that go directly *below* the operator (in math mode); no x means the subscripts % go below and to the right. NB: \P is remapped below for the complexity class P. % shortcuts for symbol names that are too long to type \newcommand{\eps}{\epsilon} \newcommand{\lam}{\lambda} \renewcommand{\l}{\ell} \newcommand{\la}{\langle} \newcommand{\ra}{\rangle} \newcommand{\wh}{\widehat} \newcommand{\wt}{\widetilde} % "blackboard-fonted" letters for the reals, naturals etc. \newcommand{\R}{\mathbb R} \newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\F}{\mathbb F} \newcommand{\Q}{\mathbb Q} \newcommand{\C}{\mathbb C} % operators that should be typeset in Roman font \newcommand{\poly}{\mathrm{poly}} \newcommand{\polylog}{\mathrm{polylog}} \newcommand{\sgn}{\mathrm{sgn}} \newcommand{\avg}{\mathop{\mathrm{avg}}} \newcommand{\val}{{\mathrm{val}}} % complexity classes \renewcommand{\P}{\mathrm{P}} \newcommand{\NP}{\mathrm{NP}} % values associated to optimization algorithm instances \newcommand{\Opt}{{\mathsf{Opt}}} \newcommand{\Alg}{{\mathsf{Alg}}} \newcommand{\Lp}{{\mathsf{Lp}}} \newcommand{\Sdp}{{\mathsf{Sdp}}} \newcommand{\Exp}{{\mathsf{Exp}}} % if you think the sum and product signs are too big in your math mode; x convention % as in the probability operators \newcommand{\littlesum}{{\textstyle \sum}} \newcommand{\littlesumx}{\mathop{{\textstyle \sum}}} \newcommand{\littleprod}{{\textstyle \prod}} \newcommand{\littleprodx}{\mathop{{\textstyle \prod}}} % horizontal line across the page \newcommand{\horz}{ \vspace{-.4in} \begin{center} \begin{tabular}{p{\textwidth}}\\ \hline \end{tabular} \end{center} } % calligraphic letters \newcommand{\calA}{{\cal A}} \newcommand{\calB}{{\cal B}} \newcommand{\calC}{{\cal C}} \newcommand{\calD}{{\cal D}} \newcommand{\calE}{{\cal E}} \newcommand{\calF}{{\cal F}} \newcommand{\calG}{{\cal G}} \newcommand{\calH}{{\cal H}} \newcommand{\calI}{{\cal I}} \newcommand{\calJ}{{\cal J}} \newcommand{\calK}{{\cal K}} \newcommand{\calL}{{\cal L}} \newcommand{\calM}{{\cal M}} \newcommand{\calN}{{\cal N}} \newcommand{\calO}{{\cal O}} \newcommand{\calP}{{\cal P}} \newcommand{\calQ}{{\cal Q}} \newcommand{\calR}{{\cal R}} \newcommand{\calS}{{\cal S}} \newcommand{\calT}{{\cal T}} \newcommand{\calU}{{\cal U}} \newcommand{\calV}{{\cal V}} \newcommand{\calW}{{\cal W}} \newcommand{\calX}{{\cal X}} \newcommand{\calY}{{\cal Y}} \newcommand{\calZ}{{\cal Z}} % bold letters (useful for random variables) % useful for Fourier analysis % if you want \newcommand{\half}{{\textstyle \frac12}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Feel free to ignore the rest of this file \def\ScribeStr{??} \def\LecStr{??} \def\LecNum{??} \def\LecTitle{??} \def\LecDate{??} \newcommand{\Scribe}[1]{\def\ScribeStr{Scribe: #1}} \newcommand{\Scribes}[1]{\def\ScribeStr{Scribes: #1}} \newcommand{\Lecturer}[1]{\def\LecStr{Lecturer: #1}} \newcommand{\Lecturers}[1]{\def\LecStr{Lecturers: #1}} \newcommand{\LectureNumber}[1]{\def\LecNum{#1}} \newcommand{\LectureDate}[1]{\def\LecDate{#1}} \newcommand{\LectureTitle}[1]{\def\LecTitle{#1}} \newdimen\headerwidth \newcommand{\MakeScribeTop}{ \noindent \begin{center} % \framebox{ \vbox{ \headerwidth=\textwidth \advance\headerwidth by -0.22in \hbox to \headerwidth {{\bf Scheduling Theory \hfill CO 454, Spring 2009} } \vspace{4mm} \hbox to \headerwidth {{\Large \hfill Assignment \AssNum \hfill}} \vspace{2mm} \hbox to \headerwidth {\hfill Due Date \LecDate \hfill} % \vspace{2mm} % \hbox to \headerwidth {{\it \LecStr \hfill \ScribeStr}} } % } \end{center} \vspace*{4mm}}