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Yu Cong 2025-05-04 00:06:02 +08:00
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.vscode/
.ds_store
*.pdf
## Core latex/pdflatex auxiliary files:
*.aux
*.lof
*.log
*.lot
*.fls
*.out
*.toc
*.fmt
*.fot
*.cb
*.cb2
.*.lb
## Intermediate documents:
*.dvi
*.xdv
*-converted-to.*
# these rules might exclude image files for figures etc.
# *.ps
# *.eps
# *.pdf
## Generated if empty string is given at "Please type another file name for output:"
.pdf
## Bibliography auxiliary files (bibtex/biblatex/biber):
*.bbl
*.bcf
*.blg
*-blx.aux
*-blx.bib
*.run.xml
## Build tool auxiliary files:
*.fdb_latexmk
*.synctex
*.synctex(busy)
*.synctex.gz
*.synctex.gz(busy)
*.pdfsync
*.rubbercache
rubber.cache
## Build tool directories for auxiliary files
# latexrun
latex.out/
## Auxiliary and intermediate files from other packages:
# algorithms
*.alg
*.loa
# achemso
acs-*.bib
# amsthm
*.thm
# beamer
*.nav
*.pre
*.snm
*.vrb
# changes
*.soc
# comment
*.cut
# cprotect
*.cpt
# elsarticle (documentclass of Elsevier journals)
*.spl
# endnotes
*.ent
# fixme
*.lox
# feynmf/feynmp
*.mf
*.mp
*.t[1-9]
*.t[1-9][0-9]
*.tfm
#(r)(e)ledmac/(r)(e)ledpar
*.end
*.?end
*.[1-9]
*.[1-9][0-9]
*.[1-9][0-9][0-9]
*.[1-9]R
*.[1-9][0-9]R
*.[1-9][0-9][0-9]R
*.eledsec[1-9]
*.eledsec[1-9]R
*.eledsec[1-9][0-9]
*.eledsec[1-9][0-9]R
*.eledsec[1-9][0-9][0-9]
*.eledsec[1-9][0-9][0-9]R
# glossaries
*.acn
*.acr
*.glg
*.glo
*.gls
*.glsdefs
*.lzo
*.lzs
*.slg
*.slo
*.sls
# uncomment this for glossaries-extra (will ignore makeindex's style files!)
# *.ist
# gnuplot
*.gnuplot
*.table
# gnuplottex
*-gnuplottex-*
# gregoriotex
*.gaux
*.glog
*.gtex
# htlatex
*.4ct
*.4tc
*.idv
*.lg
*.trc
*.xref
# hypdoc
*.hd
# hyperref
*.brf
# knitr
*-concordance.tex
# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files
# *.tikz
*-tikzDictionary
# listings
*.lol
# luatexja-ruby
*.ltjruby
# makeidx
*.idx
*.ilg
*.ind
# minitoc
*.maf
*.mlf
*.mlt
*.mtc[0-9]*
*.slf[0-9]*
*.slt[0-9]*
*.stc[0-9]*
# minted
_minted*
*.pyg
# morewrites
*.mw
# newpax
*.newpax
# nomencl
*.nlg
*.nlo
*.nls
# pax
*.pax
# pdfpcnotes
*.pdfpc
# sagetex
*.sagetex.sage
*.sagetex.py
*.sagetex.scmd
# scrwfile
*.wrt
# svg
svg-inkscape/
# sympy
*.sout
*.sympy
sympy-plots-for-*.tex/
# pdfcomment
*.upa
*.upb
# pythontex
*.pytxcode
pythontex-files-*/
# tcolorbox
*.listing
# thmtools
*.loe
# TikZ & PGF
*.dpth
*.md5
*.auxlock
# titletoc
*.ptc
# todonotes
*.tdo
# vhistory
*.hst
*.ver
# easy-todo
*.lod
# xcolor
*.xcp
# xmpincl
*.xmpi
# xindy
*.xdy
# xypic precompiled matrices and outlines
*.xyc
*.xyd
# endfloat
*.ttt
*.fff
# Latexian
TSWLatexianTemp*
## Editors:
# WinEdt
*.bak
*.sav
# Texpad
.texpadtmp
# LyX
*.lyx~
# Kile
*.backup
# gummi
.*.swp
# KBibTeX
*~[0-9]*
# TeXnicCenter
*.tps
# auto folder when using emacs and auctex
./auto/*
*.el
# expex forward references with \gathertags
*-tags.tex
# standalone packages
*.sta
# Makeindex log files
*.lpz
# xwatermark package
*.xwm
# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib
# option is specified. Footnotes are the stored in a file with suffix Notes.bib.
# Uncomment the next line to have this generated file ignored.
#*Notes.bib

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$pdf_mode = 1; # 生成PDF
$latex = 'xelatex %O %S'; # 用 xelatex 替代 latex
$pdflatex = 'xelatex %O %S'; # 用 xelatex 替代 pdflatex
$dvi_mode = 0; # 禁用DVI输出
$postscript_mode = 0; # 禁用PS输出

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\def\begin@lg{\begin{minipage}{1in}\begin{tabbing}
\quad\=\qquad\=\qquad\=\qquad\=\qquad\=\qquad\=\qquad\=\kill}
\def\end@lg{\end{tabbing}\end{minipage}}
\newenvironment{algorithm}
{\begin{tabular}{|l|}\hline\begin@lg}
{\end@lg\\\hline\end{tabular}}
\newenvironment{algo}
{\begin{center}\begin{algorithm}}
{\end{algorithm}\end{center}}
\def\argmax{\operatornamewithlimits{arg\,max}}
\def\argmin{\operatornamewithlimits{arg\,min}}

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% !TEX program = xelatex
% !TEX TS-program = xelatex
% fonts
\RequirePackage[sfdefault]{FiraSans}
\RequirePackage{FiraMono}
\renewcommand{\rmfamily}{\sffamily}
\RequirePackage[fakebold]{firamath-otf}
\RequirePackage{xeCJK}
\setCJKmainfont{Source Han Sans SC}
\RequirePackage[english]{babel}
\RequirePackage{fancyhdr} % header footer
\RequirePackage[dvipsnames]{xcolor}
\RequirePackage{bookmark}
\RequirePackage{hyperref}[colorlinks=true,urlcolor=Blue,citecolor=Green,linkcolor=BrickRed,unicode]
\RequirePackage{natbib}
\RequirePackage{graphicx} % Allows including images
\RequirePackage{booktabs} % Allows the use of \toprule, \midrule and \bottomrule in tables
% \RequirePackage{tikz}
% \usetikzlibrary{backgrounds}
% \usetikzlibrary{arrows,shapes}
% \usetikzlibrary{tikzmark} % for \tikzmarknode
% \usetikzlibrary{calc} % for computing the midpoint between two nodes, e.g. at ($(p1.north)!0.5!(p2.north)$)
% \RequirePackage[ruled,linesnumbered]{algorithm2e}
% \RequirePackage{adjustbox}
\RequirePackage{subcaption}
\RequirePackage{amsmath}
\RequirePackage{amsthm}
% \RequirePackage[utf8]{inputenc}
% \RequirePackage{CJKutf8}
% \def\zh#1{\begin{CJK}{UTF8}{gbsn}#1\end{CJK}}
\RequirePackage{aliascnt}
% a color box
\RequirePackage[breakable, theorems, skins]{tcolorbox}
\tcbset{enhanced}
\DeclareRobustCommand{\boxfill}[2][oliver!20]{%
\begin{tcolorbox}[ %% Adjust the following parameters at will.
breakable,
left=0pt,
right=0pt,
top=0pt,
bottom=0pt,
colback=#1,
colframe=#1,
width=\dimexpr\textwidth\relax,
enlarge left by=0mm,
boxsep=5pt,
arc=0pt,outer arc=0pt,
]
#2
\end{tcolorbox}
}
\definecolor{beamer@simple@color}{RGB}{12 72 66} % bluegreen
\DeclareOptionBeamer{gray}{\definecolor{beamer@simple@color}{gray}{#1}}
\DeclareOptionBeamer{rgb}{\definecolor{beamer@simple@color}{rgb}{#1}}
\DeclareOptionBeamer{RGB}[{12 72 0}]{\definecolor{beamer@simple@color}{RGB}{#1}}
\DeclareOptionBeamer{HTML}{\definecolor{beamer@simple@color}{HTML}{#1}}
\DeclareOptionBeamer{cmyk}{\definecolor{beamer@simple@color}{cmyk}{#1}}
\DeclareOptionBeamer{cmy}{\definecolor{beamer@simple@color}{cmy}{#1}}
\DeclareOptionBeamer{named}{\definecolor{beamer@simple@color}{named}{#1}}
\DeclareOptionBeamer{hsb}{\definecolor{beamer@simple@color}{hsb}{#1}}
\ProcessOptionsBeamer
\definecolor{oliver}{rgb}{0.33, 0.42, 0.18}
% footline
% delete navigation below
\setbeamertemplate{navigation symbols}{}
\useoutertheme{tree}
\makeatletter
\setbeamertemplate{headline}
{%
\begin{beamercolorbox}[wd=\paperwidth,colsep=1.5pt]{upper separation line head}
\end{beamercolorbox}
\begin{beamercolorbox}[wd=\paperwidth,ht=2.5ex,dp=1.125ex,%
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\usebeamerfont{title in head/foot}\insertshorttitle
\usebeamerfont{section in head/foot}%
\ifbeamer@tree@showhooks
\setbox\beamer@tempbox=\hbox{\insertsectionhead}%
\ifdim\wd\beamer@tempbox>1pt%
\hskip2pt\raise1.9pt\hbox{\vrule width 5pt height0.4pt}%
\hskip1pt%
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\else%
\hskip6pt%
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\insertsectionhead
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\begin{beamercolorbox}[wd=\paperwidth,colsep=1.5pt]{lower separation line head}
\end{beamercolorbox}
}
\makeatother
% footline color
\setbeamercolor{author in head/foot}{fg=black, bg=mygrey!5!white}
\setbeamercolor{title in head/foot}{fg=black, bg=mygrey!5!white}
\setbeamercolor*{title}{fg=beamer@simple@color, bg=white}
% item settings
\setbeamertemplate{itemize item}{$\color{beamer@simple@color}\bullet$}
\setbeamertemplate{itemize subitem}{$\color{beamer@simple@color}\bullet$}
\setbeamertemplate{enumerate items}[square]
\setbeamertemplate{section in toc}[sections numbered]
\setbeamertemplate{subsection in toc}[square]
% color definition
\definecolor{mygrey}{rgb}{0.52, 0.52, 0.51}
\setbeamercolor{structure}{fg=beamer@simple@color, bg=mygrey!10!white}
\setbeamercolor{frametitle}{fg=beamer@simple@color, bg=white}
\setbeamercolor{block title}{fg=beamer@simple@color,bg=white}
\setbeamercolor{block body}{fg=black,bg=white}
\setbeamercolor{block body alerted}{bg=white}
\setbeamercolor{block title alerted}{fg=beamer@simple@color,bg=white}
\setbeamercolor{alerted text}{fg=beamer@simple@color}
\setbeamerfont{block title alerted}{series=\mdseries}
\setbeamerfont{alerted text}{series=\bfseries\boldmath}
\hypersetup{colorlinks=true,linkcolor=,citecolor=Green,urlcolor=oliver}
% \usefonttheme[onlymath]{serif}
\setbeamerfont{frametitle}{series=\bfseries\boldmath}
\setbeamerfont{block title}{series=\bfseries\boldmath}
\setbeamerfont{title}{series=\bfseries\boldmath}
\setbeamertemplate{frametitle}{\vskip2pt\hskip-6pt\underline{\insertframetitle}} % add line under frametitle
% theorem env
\setbeamertemplate{theorem begin}{%
{
\vspace{5pt}%
\usebeamerfont*{block title}%
\selectfont%
\usebeamercolor[fg]{block title}%
\textbf{%
\inserttheoremname
\inserttheoremnumber
\ifx \inserttheoremaddition \empty \else\ [\inserttheoremaddition]\fi
}
}
}
\setbeamertemplate{theorem end}{\vspace{5pt}}
% proof env
\setbeamertemplate{proof begin}{%
{\vspace{5pt}
\usebeamercolor[fg]{block title}
\textit{\textbf{Proof:}}}
}
\setbeamertemplate{proof end}{
\qedhere
\vspace{5pt}
}
% more theorem env
\newtheorem{observation}{Observation}
\newtheorem{question}{Question}
% ----------------------------------------------------------------------
% Simple math stuff
% ----------------------------------------------------------------------
\renewcommand{\subset}{\subseteq}
% ---- SYMBOLS ----
\let\e\varepsilon % a ``real'' epsilon — better yet, just use Unicode ε.
%
% I give up. These are in the wrong font, but my kludged versions
% LOOK like kludges, especially \Z, \Q, and \C.
%
\def\Real{\mathbb{R}}
\def\Proj{\mathbb{P}}
\def\Hyper{\mathbb{H}}
\def\Integer{\mathbb{Z}}
\def\Natural{\mathbb{N}}
\def\Complex{\mathbb{C}}
\def\Rational{\mathbb{Q}}
\let\N\Natural
\let\Q\Rational
\let\R\Real
\let\Z\Integer
\def\Rd{\Real^d}
\def\RP{\Real\Proj}
\def\CP{\Complex\Proj}
% ---- OPERATORS (requires amsmath) ----
\def\aff{\operatorname{aff}}
\def\area{\operatorname{area}}
\def\argmax{\operatornamewithlimits{arg\,max}}
\def\argmin{\operatornamewithlimits{arg\,min}}
\def\Aut{\operatorname{Aut}} % Automorphism group
\def\card{\operatorname{card}} % cardinality, deprecated for \abs
\def\conv{\operatorname{conv}}
\def\E{\operatorname{E}} % Expectation: $\E[X]$ (like \Pr)
\def\EE{\operatornamewithlimits{E}}
\def\Hom{\operatorname{Hom}} % Homomorphism group
\def\id{\operatorname{id}} % identity
\def\im{\operatorname{im}} % image
\def\lcm{\operatorname{lcm}}
\def\lfs{\operatorname{lfs}} % local feature size
\def\poly{\operatorname{poly}}
\def\polylog{\operatorname{polylog}}
\def\rank{\operatorname{rank}}
\def\rel{\operatorname{rel\,}} % relative (interior, boundary, etc.)
\def\sgn{\operatorname{sgn}}
\def\vol{\operatorname{vol}} % volume
\def\fp#1{^{\underline{#1}}} % falling powers: $n\fp{d}$
\def\rp#1{^{\overline{#1}}} % rising powers: $n\rp{d}$
\def\setsymdiff{\operatorname{\triangle}}
% % --- Darts and fences ---
% % less nice replacements for stmaryrd characters
% \@ifundefined{shortrightarrow}{\let\shortrightarrow\rightarrow}{}
% \@ifundefined{shortleftarrow}{\let\shortleftarrow\leftarrow}{}
% \@ifundefined{shortuparrow}{\let\shortuparrow\uparrow}{}
% \@ifundefined{shortdownarrow}{\let\shortdownarrow\downarrow}{}
\def\arcto{\mathord\shortrightarrow}
\def\arcfrom{\mathord\shortleftarrow}
\def\arc#1#2{#1\arcto#2}
\def\cra#1#2{#1\mathord\shortleftarrow#2}
\def\fence#1#2{#1\mathord\shortuparrow#2}
\def\ecnef#1#2{#1\mathord\shortdownarrow#2}
% --- Cheap displaystyle operators ---
\def\Frac#1#2{{\displaystyle\frac{#1}{#2}}}
\def\Sum{\sum\limits}
\def\Prod{\prod\limits}
\def\Union{\bigcup\limits}
\def\Inter{\bigcap\limits}
\def\Lor{\bigvee\limits}
\def\Land{\bigwedge\limits}
\def\Lim{\lim\limits}
\def\Max{\max\limits}
\def\Min{\min\limits}
% ---- RELATORS ----
\def\deq{\stackrel{\scriptscriptstyle\triangle}{=}} % Use := instead.
\def\into{\DOTSB\hookrightarrow} % = one-to-one
\def\onto{\DOTSB\twoheadrightarrow}
\def\inonto{\DOTSB\lhook\joinrel\twoheadrightarrow}
\def\from{\leftarrow}
\def\tofrom{\leftrightarrow}
\def\mapsfrom{\mathrel{\reflectbox{$\mapsto$}}}
\def\longmapsfrom{\mathrel{\reflectbox{$\longmapsto$}}}
% ---- DELIMITER PAIRS ----
% --- always self-scaling delmiter pairs ---
\def\set#1{\left\{ #1 \right\}}
\def\floor#1{\left\lfloor #1 \right\rfloor}
\def\ceil#1{\left\lceil #1 \right\rceil}
\def\seq#1{\left\langle #1 \right\rangle}
\def\abs#1{\left| #1 \right|}
\def\norm#1{\left\| #1 \right\|}
\def\paren#1{\left( #1 \right)} % need better macro name!
\def\brack#1{\left[ #1 \right]} % need better macro name!
\def\indic#1{\left[ #1 \right]} % indicator variable; Iverson notation

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\documentclass{beamer}
\title[Edge Conn Interdiction]{Faster FPTAS for Edge Connectivity Interdiction}
\date{\today}
\author{丛宇}
% \AtBeginSection[]{
% \frame{\frametitle{Outline}\tableofcontents[currentsection,
% subsectionstyle=show/show/shaded]}
% }
\usetheme{Simple}
\usepackage{algo}
\begin{document}
\begin{frame}[plain]
% Print the title page as the first slide
\titlepage
\end{frame}
\begin{frame}[plain]{Plan}
\tableofcontents
\end{frame}
\section{Connectivity Interdiction}
\begin{frame}{Edge Connectivity \& Cut}
\begin{definition}
Let $G=(V,E)$ be a undirected connected graph. The minimum cut of $G$ is the minimum set of edges whose removal breaks the connectivity of $G$.
\end{definition}
The edge connectivity of $G$ = $|\text{mincut of $G$}|-1$.
\newline
Edge connectivity is an important measure of network reliability. The greater the edge connectivity, the more difficult it is to break the network's connectivity.
\newline
Now suppose that we want to attack the network. To what extent can we decrease the size of the min-cut by removing a limited set of edges?
\end{frame}
\begin{frame}{Interdiction}
\begin{problem}[edge connectivity interdiction]
The input is a graph $G=(V,E)$ with edge weights $w:E\to \Z_+$ and edge removal cost $c:E\to \Z_+$ and a budget $b\in \Z_+$. The goal is to find a interdiction set $F\subset E$ with $c(F)\leq b$ that minimizes the mincut in $G-F$.
\end{problem}
\end{frame}
\begin{frame}{Examples}
\begin{figure}
Examples for containing knapsack and for unweighted easy case.
\end{figure}
\end{frame}
\begin{frame}{Prevous Works}
Zenklusen \citep{zenklusen_connectivity_2014} first studied this problem and showed the following results:
\begin{itemize}
\item A PTAS\footnote{polynomial time approximation scheme} for edge connectivity interdiction;
\item A $\tilde{O}(m^2 n^4)$ algorithm for the unit cost case\footnote{$\tilde{O}$ hides polylog factors}.
\end{itemize}
Later \citep{vygen_fptas_2024} discovered an FPTAS\footnote{fully PTAS} with time complexity $\tilde{O}(m^2 n^4/\epsilon)$.
\end{frame}
\section{FPTAS}
\begin{frame}{placeholder}
\end{frame}
\section{LP Perspective}
\begin{frame}{placeholder}
\end{frame}
\begin{frame}{References}
\bibliographystyle{plainnat}
\bibliography{ref}
\end{frame}
\end{document}

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@inproceedings{vygen_fptas_2024,
address = {Cham},
title = {An {FPTAS} for {Connectivity} {Interdiction}},
volume = {14679},
isbn = {978-3-031-59834-0 978-3-031-59835-7},
url = {https://link.springer.com/10.1007/978-3-031-59835-7_16},
language = {en},
urldate = {2024-11-04},
booktitle = {Integer {Programming} and {Combinatorial} {Optimization}},
publisher = {Springer Nature Switzerland},
author = {Huang, Chien-Chung and Obscura Acosta, Nidia and Yingchareonthawornchai, Sorrachai},
editor = {Vygen, Jens and Byrka, Jarosław},
year = {2024},
doi = {10.1007/978-3-031-59835-7_16},
note = {Series Title: Lecture Notes in Computer Science},
pages = {210--223},
}
@article{zenklusen_connectivity_2014,
title = {Connectivity interdiction},
volume = {42},
issn = {01676377},
url = {http://dx.doi.org/10.1016/j.orl.2014.07.010},
doi = {10.1016/j.orl.2014.07.010},
number = {6-7},
journal = {Operations Research Letters},
author = {Zenklusen, Rico},
year = {2014},
note = {Publisher: Elsevier B.V.},
keywords = {Approximation algorithms, Interdiction problems, Multi-objective optimization, Robust optimization},
pages = {450--454},
}