The Asymmetric Traveling Salesman Path LP Has Constant Integrality Ratio

被引：2
|
作者：
Koehne, Anna [1 ]
Traub, Vera [1 ]
Vygen, Jens [1 ]
机构：
[1] Univ Bonn, Res Inst Discrete Math, Bonn, Germany
来源：
INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION, IPCO 2019 | 2019年 / 11480卷
关键词：
D O I：
10.1007/978-3-030-17953-3_22
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We show that the classical LP relaxation of the asymmetric traveling salesman path problem (ATSPP) has constant integrality ratio. If rho(ATSP) and rho(ATSPP) denote the integrality ratios for the asymmetric TSP and its path version, then rho(ATSPP) <= 4 rho(ATSP) - 3. We prove an even better bound for node-weighted instances: if the integrality ratio for ATSP on node-weighted instances is rho(NW)(ATSP), then the integrality ratio for ATSPP on node-weighted instances is at most 2 rho(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：288 / 298
页数：11
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