On two geometric problems related to the travelling salesman problem

Papadimitriou, CH; Vazirani, UV

dc.contributor.author	Papadimitriou, CH	en
dc.contributor.author	Vazirani, UV	en
dc.date.accessioned	2014-03-01T01:06:17Z
dc.date.available	2014-03-01T01:06:17Z
dc.date.issued	1984	en
dc.identifier.issn	0196-6774	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9293
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0037854822&partnerID=40&md5=2b9adbf7b7d0bc1017842a364d2d1131	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.classification	Mathematics, Applied	en
dc.title	On two geometric problems related to the travelling salesman problem	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1984	en
heal.abstract	The degree-K Minimum Spanning Tree (MST) problem asks for the minimum length spanning tree that has no vertex of degree greater than K. The Euclidean degree-K MST problem is known to be tractable for K ≥ 5; the degree-2 MST is simply the Euclidean path-TSP, which is NP-complete. It is proved that the Euclidean degree-3 MST problem is also NP-complete, thus leaving open only the case for K = 4. Among the most illustrious approximation algorithms is the heuristic for the Euclidean TSP due to Christofides. It is proved that implementing the ""shortcutting phase"" of Christofides' algorithm optimally is NP-hard (even so, Christofides' algorithm guarantees a tour which is no more than 50% longer than the optimal one). © 1984.	en
heal.publisher	ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS	en
heal.journalName	Journal of Algorithms	en
dc.identifier.isi	ISI:A1984SV82600006	en
dc.identifier.volume	5	en
dc.identifier.issue	2	en
dc.identifier.spage	231	en
dc.identifier.epage	246	en