On the path-width of integer linear programming

被引：0

作者：

Enea, Constantin ^{[1
,2
]}

Habermehl, Peter ^{[1
,2
]}

Inverso, Omar ^{[3
]}

Parlato, Gennaro ^{[4
]}

机构：

[1] Univ Paris Diderot, IRIF, F-75205 Paris 13, France

[2] CNRS, F-75205 Paris 13, France

[3] Gran Sasso Sci Inst, Viale Francesco Crispi 7, Laquila, Italy

[4] Univ Southampton, Sch Elect & Comp Sci, Southampton SO9 5NH, Hants, England

来源：

INFORMATION AND COMPUTATION | 2017年 / 253卷

关键词：

Integer linear programming; Bounded path-width; First-order logic on graphs; Automata; MODEL CHECKING;

D O I：

10.1016/j.ic.2016.07.010

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it. However, one of these graphs is of path-width at most 2n, where n is the number of variables in the instance. Since FO is decidable on graphs of bounded path-width, we obtain an alternative decidability result for ILP. The technique we use underlines a common principle to prove decidability which has previously been employed for automata with auxiliary storage. We also show how this new result links to automata theory and program verification. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：257 / 271

页数：15

共 50 条

[21] ON 3-CONNECTED GRAPHS OF PATH-WIDTH AT MOST THREE
Ding, Guoli
Dziobiak, Stan
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2013, 27 (03) : 1514 - 1526
[22] THE VERTEX SEPARATION NUMBER OF A GRAPH EQUALS ITS PATH-WIDTH
KINNERSLEY, NG
INFORMATION PROCESSING LETTERS, 1992, 42 (06) : 345 - 350
[23] MINIMAL ACYCLIC FORBIDDEN MINORS FOR THE FAMILY OF GRAPHS WITH BOUNDED PATH-WIDTH
TAKAHASHI, A
UENO, S
KAJITANI, Y
DISCRETE MATHEMATICS, 1994, 127 (1-3) : 293 - 304
[24] An integer linear programming approach for bilinear integer programming
Freire, Alexandre S.
Moreno, Eduardo
Vielma, Juan Pablo
OPERATIONS RESEARCH LETTERS, 2012, 40 (02) : 74 - 77
[25] Crossing-number critical graphs have bounded path-width
Hlineny, P
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2003, 88 (02) : 347 - 367
[26] INTEGER LINEAR PROGRAMMING
PETERSEN, CC
JOURNAL OF INDUSTRIAL ENGINEERING, 1967, 18 (08): : 456 - &
[27] LINEAR INTEGER PROGRAMMING
SWANEK, JJ
REPORT OF NRL PROGRESS, 1974, (NOV): : 17 - 17
[28] Efficient Mixed Integer Linear Programming Approaches to Dynamic Path Restoration
Rubtsov, Alexander
Bauwens, Bruno
Shmelkin, Dmitri
Rudenko, Elizaveta
Lavrov, Alexey
2024 IEEE INTERNATIONAL BLACK SEA CONFERENCE ON COMMUNICATIONS AND NETWORKING, BLACKSEACOM 2024, 2024, : 146 - 152
[29] First Order Limits of Sparse Graphs: Plane Trees and Path-Width
Gajarsky, Jakub
Hlineny, Petr
Kaiser, Tomas
Kral, Daniel
Kupec, Martin
Obdrzalek, Jan
Ordyniak, Sebastian
Tuma, Vojtech
RANDOM STRUCTURES & ALGORITHMS, 2017, 50 (04) : 612 - 635
[30] Learning Bounded Tree-width Bayesian Networks using Integer Linear Programming
Parviainen, Pekka
Farahani, Hossein Shahrabi
Lagergren, Jens
ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 33, 2014, 33 : 751 - 759

← 1 2 3 4 5 →