Robust subgraphs for trees and paths

Refael Hassin*, Danny Segev

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Consider a graph problem which is associated with a parameter, for example, that of finding a longest tour spanning k vertices. The following question is natural: Is there a small subgraph which contains optimal or near optimal solution for every possible value of the given parameter? Such a subgraph is said to be robust. In this paper we consider the problems of finding heavy paths and heavy trees of k edges. In these two cases we prove surprising bounds on the size of a robust subgraph for a variety of approximation ratios. For both problems we show that in every complete weighted graph on n vertices there exists a subgraph with approximately α/1-α2n edges which contains an α-approximate solution for every k = 1, . . . , n - 1. In the analysis of the tree problem we also describe a new result regarding balanced decomposition of trees. In addition, we consider variations in which the subgraph itself is restricted to be a path or a tree. For these problems we describe polynomial time algorithms and corresponding proofs of negative results.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsTorben Hagerup, Jyrki Katajainen
PublisherSpringer Verlag
Pages51-63
Number of pages13
ISBN (Electronic)3540223398, 9783540223399
DOIs
StatePublished - 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3111
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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