Approximation algorithms for Euclidean group TSP

Khaled Elbassioni*, Aleksei V. Fishkin, Nabil H. Mustafa, René Sitters

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


In the Euclidean group Traveling Salesman Problem (TSP), we are given a set of points P in the plane and a set of m connected regions, each containing at least one point of P. We want to find a tour of minimum length that visits at least one point in each region. This unifies the TSP with Neighborhoods and the Group Steiner Tree problem. We give a (9.1α + 1)-approximation algorithm for the case when the regions are disjoint α-fat objects with possibly varying size. This considerably improves the best results known, in this case, for both the group Steiner tree problem and the TSP with Neighborhoods problem. We also give the first O(1)-approximation algorithm for the problem with intersecting regions.

Original languageEnglish
Pages (from-to)1115-1126
Number of pages12
JournalLecture Notes in Computer Science
Publication statusPublished - 2005


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