Minimum-diameter covering problems

Esther M. Arkin; Refael Hassin

doi:10.1002/1097-0037(200010)36:3<147::AID-NET1>3.0.CO;2-M

Minimum-diameter covering problems

Esther M. Arkin^*, Refael Hassin

^*Corresponding author for this work

School of Mathematical Sciences

Stony Brook University

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

A set V and a collection of (possibly nondisjoint) subsets are given. Also given is a real matrix describing distances between elements of V. A cover is a subset of V containing at least one representative from each subset. The multiple-choice minimum-diameter problem is to select a cover of minimum diameter. The diameter is defined as the maximum distance between any pair of elements in the cover. The multiple-choice dispersion problem, which is closely related, asks us to maximize the minimum distance between any pair of elements in the cover. The problems are NP-hard. We present polynomial time algorithms for approximating special cases and generalizations of these basic problems, and we prove in other cases that no such algorithms exist (assuming P ≉ NP).

Original language	English
Pages (from-to)	147-155
Number of pages	9
Journal	Networks
Volume	36
Issue number	3
DOIs	https://doi.org/10.1002/1097-0037(200010)36:3<147::AID-NET1>3.0.CO;2-M
State	Published - Oct 2000

Keywords

Approximation algorithms
Covering problems
Graph diameter
NP-complete

Access to Document

10.1002/1097-0037(200010)36:3<147::AID-NET1>3.0.CO;2-M

Cite this

@article{05c62994d4a145f7ba5707036aba4dcf,

title = "Minimum-diameter covering problems",

abstract = "A set V and a collection of (possibly nondisjoint) subsets are given. Also given is a real matrix describing distances between elements of V. A cover is a subset of V containing at least one representative from each subset. The multiple-choice minimum-diameter problem is to select a cover of minimum diameter. The diameter is defined as the maximum distance between any pair of elements in the cover. The multiple-choice dispersion problem, which is closely related, asks us to maximize the minimum distance between any pair of elements in the cover. The problems are NP-hard. We present polynomial time algorithms for approximating special cases and generalizations of these basic problems, and we prove in other cases that no such algorithms exist (assuming P ≉ NP).",

keywords = "Approximation algorithms, Covering problems, Graph diameter, NP-complete",

author = "Arkin, {Esther M.} and Refael Hassin",

year = "2000",

month = oct,

doi = "10.1002/1097-0037(200010)36:3<147::AID-NET1>3.0.CO;2-M",

language = "אנגלית",

volume = "36",

pages = "147--155",

journal = "Networks",

issn = "0028-3045",

publisher = "Wiley-Liss Inc.",

number = "3",

}

TY - JOUR

T1 - Minimum-diameter covering problems

AU - Arkin, Esther M.

AU - Hassin, Refael

PY - 2000/10

Y1 - 2000/10

N2 - A set V and a collection of (possibly nondisjoint) subsets are given. Also given is a real matrix describing distances between elements of V. A cover is a subset of V containing at least one representative from each subset. The multiple-choice minimum-diameter problem is to select a cover of minimum diameter. The diameter is defined as the maximum distance between any pair of elements in the cover. The multiple-choice dispersion problem, which is closely related, asks us to maximize the minimum distance between any pair of elements in the cover. The problems are NP-hard. We present polynomial time algorithms for approximating special cases and generalizations of these basic problems, and we prove in other cases that no such algorithms exist (assuming P ≉ NP).

AB - A set V and a collection of (possibly nondisjoint) subsets are given. Also given is a real matrix describing distances between elements of V. A cover is a subset of V containing at least one representative from each subset. The multiple-choice minimum-diameter problem is to select a cover of minimum diameter. The diameter is defined as the maximum distance between any pair of elements in the cover. The multiple-choice dispersion problem, which is closely related, asks us to maximize the minimum distance between any pair of elements in the cover. The problems are NP-hard. We present polynomial time algorithms for approximating special cases and generalizations of these basic problems, and we prove in other cases that no such algorithms exist (assuming P ≉ NP).

KW - Approximation algorithms

KW - Covering problems

KW - Graph diameter

KW - NP-complete

UR - http://www.scopus.com/inward/record.url?scp=0034288913&partnerID=8YFLogxK

U2 - 10.1002/1097-0037(200010)36:3<147::AID-NET1>3.0.CO;2-M

DO - 10.1002/1097-0037(200010)36:3<147::AID-NET1>3.0.CO;2-M

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0034288913

SN - 0028-3045

VL - 36

SP - 147

EP - 155

JO - Networks

JF - Networks

IS - 3

ER -

Minimum-diameter covering problems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this