NDLI: Reassembling Trees for the Traveling Salesman

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Vygen, Jens
Copyright Year	2016
Abstract	Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, $s$-$t$-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written as convex combination of spanning trees. The main argument then is that randomly sampling a tree from such a distribution and then completing the tree to a tour at minimum cost yields a better approximation guarantee than simply taking a minimum cost spanning tree (as in Christofides' algorithm). We argue that an additional step can help: reassembling the spanning trees before sampling. Exchanging two edges in a pair of spanning trees can improve their properties under certain conditions. We demonstrate the usefulness for the metric $s$-$t$-path TSP by devising a deterministic polynomial-time algorithm that improves on Sebö's previously best approximation ratio of $\frac{8}{5}$.
Starting Page	875
Ending Page	894
Page Count	20
File Format	PDF
ISSN	08954801
DOI	10.1137/15M1010531
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	2
Volume Number	30
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-05-05
Access Restriction	Subscribed
Subject Keyword	traveling salesman problem spanning tree $s$-$t$-path TSP approximation algorithm Combinatorial optimization
Content Type	Text
Resource Type	Article
Subject	Mathematics

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On the Metric $s$--$t$ Path Traveling Salesman Problem

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