Linear time algorithms for computing the most reliable source on an unreliable tree network

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Given a tree network with n vertices where each edge has an operational probability, we are interested in finding a vertex on the tree whose expected number of reachable vertices is maximum. This problem was studied in Networks 27 (1996) 219-237, where an O(n3) time algorithm and an O(n2) time algorithm were proposed. In this paper, we present an O(n) time algorithm for the same problem, improving the previously best algorithm by a factor of O(n). We also study a max-min version of the problem and propose an O(n) time algorithm for this problem as well. Examples are provided to illustrate the algorithms.

Original languageEnglish (US)
Pages (from-to)37-45
Number of pages9
JournalNetworks
Volume30
Issue number1
StatePublished - Aug 1997
Externally publishedYes

Keywords

  • Algorithms
  • Centers
  • Medians
  • Network reliability
  • Time complexity
  • Tree networks

ASJC Scopus subject areas

  • Hardware and Architecture

Cite this

Linear time algorithms for computing the most reliable source on an unreliable tree network. / Xue, Guoliang.

In: Networks, Vol. 30, No. 1, 08.1997, p. 37-45.

Research output: Contribution to journalArticle

@article{dcef92c84ebd44cdb53a236945f52173,
title = "Linear time algorithms for computing the most reliable source on an unreliable tree network",
abstract = "Given a tree network with n vertices where each edge has an operational probability, we are interested in finding a vertex on the tree whose expected number of reachable vertices is maximum. This problem was studied in Networks 27 (1996) 219-237, where an O(n3) time algorithm and an O(n2) time algorithm were proposed. In this paper, we present an O(n) time algorithm for the same problem, improving the previously best algorithm by a factor of O(n). We also study a max-min version of the problem and propose an O(n) time algorithm for this problem as well. Examples are provided to illustrate the algorithms.",
keywords = "Algorithms, Centers, Medians, Network reliability, Time complexity, Tree networks",
author = "Guoliang Xue",
year = "1997",
month = "8",
language = "English (US)",
volume = "30",
pages = "37--45",
journal = "Networks",
issn = "0028-3045",
publisher = "Wiley-Liss Inc.",
number = "1",

}

TY - JOUR

T1 - Linear time algorithms for computing the most reliable source on an unreliable tree network

AU - Xue, Guoliang

PY - 1997/8

Y1 - 1997/8

N2 - Given a tree network with n vertices where each edge has an operational probability, we are interested in finding a vertex on the tree whose expected number of reachable vertices is maximum. This problem was studied in Networks 27 (1996) 219-237, where an O(n3) time algorithm and an O(n2) time algorithm were proposed. In this paper, we present an O(n) time algorithm for the same problem, improving the previously best algorithm by a factor of O(n). We also study a max-min version of the problem and propose an O(n) time algorithm for this problem as well. Examples are provided to illustrate the algorithms.

AB - Given a tree network with n vertices where each edge has an operational probability, we are interested in finding a vertex on the tree whose expected number of reachable vertices is maximum. This problem was studied in Networks 27 (1996) 219-237, where an O(n3) time algorithm and an O(n2) time algorithm were proposed. In this paper, we present an O(n) time algorithm for the same problem, improving the previously best algorithm by a factor of O(n). We also study a max-min version of the problem and propose an O(n) time algorithm for this problem as well. Examples are provided to illustrate the algorithms.

KW - Algorithms

KW - Centers

KW - Medians

KW - Network reliability

KW - Time complexity

KW - Tree networks

UR - http://www.scopus.com/inward/record.url?scp=0039330085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039330085&partnerID=8YFLogxK

M3 - Article

VL - 30

SP - 37

EP - 45

JO - Networks

JF - Networks

SN - 0028-3045

IS - 1

ER -