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Minimum spanning tree with neighborhoods

  • SUNY Buffalo

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

31 Scopus citations

Abstract

We consider a natural generalization of the classical minimum spanning tree problem called Minimum Spanning Tree with Neighborhoods (MSTN) which seeks a tree of minimum length to span a set of 2D regions called neighborhoods. Each neighborhood contributes exact one node to the tree, and the MSTN has the minimum total length among all possible trees spanning the set of nodes. We prove the NP-hardness of this problem for the case in which the neighborhoods are a set of disjoint discs and rectangles. When the regions considered are a set of disjoint 2D unit discs, we present the following approximation results: (I)A simple algorithm that achieves an approximation ratio of 7.4; (2) Lower bounds and two 3-approximation algorithms; (3) A PTAS for this problem. Our algorithms can be easily generalized to higher dimensions.

Original languageEnglish
Title of host publicationAlgorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings
PublisherSpringer Verlag
Pages306-316
Number of pages11
ISBN (Print)9783540728689
DOIs
StatePublished - 2007
Event3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007 - Portland, OR, United States
Duration: Jun 6 2007Jun 8 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4508 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007
Country/TerritoryUnited States
CityPortland, OR
Period06/6/0706/8/07

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