The asymmetric traveling salesman path LP has constant integrality ratio

被引：1
|
作者：
Koehne, Anna [1 ,2 ]
Traub, Vera [1 ,2 ]
Vygen, Jens [1 ,2 ]
机构：
[1] Univ Bonn, Res Inst Discrete Math, Bonn, Germany
[2] Univ Bonn, Hausdorff Ctr Math, Bonn, Germany
来源：
MATHEMATICAL PROGRAMMING | 2020年 / 183卷 / 1-2期
关键词：
Asymmetric traveling salesman problem; Integrality gap; Linear programming relaxations;
D O I：
10.1007/s10107-019-01450-8
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We show that the classical LP relaxation of the asymmetric traveling salesman path problem (ATSPP) has constant integrality ratio. If.ATSP and.ATSPP denote the integrality ratios for the asymmetric TSP and its path version, then.ATSPP = 4.ATSP - 3. We prove an even better bound for node-weighted instances: if the integrality ratio for ATSP on node-weighted instances is.NWATSP, then the integrality ratio for ATSPP on node-weighted instances is at most 2.NW ATSP - 1. Moreover, we show that for ATSP node-weighted instances and unweighted digraph instances are almost equivalent. From this we deduce a lower bound of 2 on the integrality ratio of unweighted digraph instances.
引用
收藏
页码：379 / 395
页数：17
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