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

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