The approximability of partial vertex covers in trees

Vahan Mkrtchyan, Ojas Parekh, Danny Segev, K. Subramani

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

Abstract

Motivated by applications in risk management of computational systems, we focus our attention on a special case of the partial vertex cover problem, where the underlying graph is assumed to be a tree. Here, we consider four possible versions of this setting, depending on whether vertices and edges are weighted or not. Two of these versions, where edges are assumed to be unweighted, are known to be polynomial-time solvable. However, the computational complexity of this problem with weighted edges, and possibly with weighted vertices, has not been determined yet. The main contribution of this paper is to resolve these questions by fully characterizing which variants of partial vertex cover remain intractable in trees, and which can be efficiently solved. In particular, we propose a pseudo-polynomial DP-based algorithm for the most general case of having weights on both edges and vertices, which is proven to be NP-hard. This algorithm provides a polynomialtime solution method when weights are limited to edges, and combined with additional scaling ideas, leads to an FPTAS for the general case. A secondary contribution of this work is to propose a novel way of using centroid decompositions in trees, which could be useful in other settings as well.

Original languageEnglish
Title of host publicationSOFSEM 2017
Subtitle of host publicationTheory and Practice of Computer Science - 43rd International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings
EditorsChristel Baier, Mark van den Brand, Johann Eder, Mike Hinchey, Tiziana Margaria, Bernhard Steffen
PublisherSpringer Verlag
Pages350-360
Number of pages11
ISBN (Print)9783319519623
DOIs
StatePublished - 2017
Event43rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2017 - Limerick, Ireland
Duration: 16 Jan 201720 Jan 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10139 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference43rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2017
Country/TerritoryIreland
CityLimerick
Period16/01/1720/01/17

Bibliographical note

Funding Information:
K. Subramani—Supported by the National Science Foundation through Award CCF-1305054 and also supported by the Air Force of Scientific Research through Award FA9550-12-1-0199.

Funding Information:
V. Mkrtchyan—This research has been supported in part by the Air Force of Scientific Research through Award FA9550-12-1-0199.

Publisher Copyright:
© Springer International Publishing AG 2017.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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