Searching for a black hole in synchronous tree networks

Jurek Czyzowicz, Dariusz Kowalski, Euripides Markou, Andrzej Pelc

Research output: Contribution to journalArticle

Abstract

A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous tree network, assuming an upper bound on the time of any edge traversal by an agent. The minimum number of agents capable of identifying a black hole is two. For a given tree and given starting node we are interested in the fastest-possible black hole search by two agents. For arbitrary trees we give a 5/3-approximation algorithm for this problem. We give optimal black hole search algorithms for two 'extreme' classes of trees: the class of lines and the class of trees in which any internal node (including the root which is the starting node) has at least two children.

Original languageEnglish (US)
Pages (from-to)595-619
Number of pages25
JournalCombinatorics Probability and Computing
Volume16
Issue number4
DOIs
StatePublished - Jul 1 2007
Externally publishedYes

Fingerprint

Tree Networks
Mobile agents
Approximation algorithms
Black Holes
Vertex of a graph
Mobile Agent
Stationary Process
Search Algorithm
Approximation Algorithms
Extremes
Trace
Roots
Upper bound
Internal
Line
Arbitrary
Class

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Searching for a black hole in synchronous tree networks. / Czyzowicz, Jurek; Kowalski, Dariusz; Markou, Euripides; Pelc, Andrzej.

In: Combinatorics Probability and Computing, Vol. 16, No. 4, 01.07.2007, p. 595-619.

Research output: Contribution to journalArticle

Czyzowicz, Jurek ; Kowalski, Dariusz ; Markou, Euripides ; Pelc, Andrzej. / Searching for a black hole in synchronous tree networks. In: Combinatorics Probability and Computing. 2007 ; Vol. 16, No. 4. pp. 595-619.
@article{c3ba23d04c19482e97ca823ce05043a4,
title = "Searching for a black hole in synchronous tree networks",
abstract = "A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous tree network, assuming an upper bound on the time of any edge traversal by an agent. The minimum number of agents capable of identifying a black hole is two. For a given tree and given starting node we are interested in the fastest-possible black hole search by two agents. For arbitrary trees we give a 5/3-approximation algorithm for this problem. We give optimal black hole search algorithms for two 'extreme' classes of trees: the class of lines and the class of trees in which any internal node (including the root which is the starting node) has at least two children.",
author = "Jurek Czyzowicz and Dariusz Kowalski and Euripides Markou and Andrzej Pelc",
year = "2007",
month = "7",
day = "1",
doi = "10.1017/S0963548306008133",
language = "English (US)",
volume = "16",
pages = "595--619",
journal = "Combinatorics Probability and Computing",
issn = "0963-5483",
publisher = "Cambridge University Press",
number = "4",

}

TY - JOUR

T1 - Searching for a black hole in synchronous tree networks

AU - Czyzowicz, Jurek

AU - Kowalski, Dariusz

AU - Markou, Euripides

AU - Pelc, Andrzej

PY - 2007/7/1

Y1 - 2007/7/1

N2 - A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous tree network, assuming an upper bound on the time of any edge traversal by an agent. The minimum number of agents capable of identifying a black hole is two. For a given tree and given starting node we are interested in the fastest-possible black hole search by two agents. For arbitrary trees we give a 5/3-approximation algorithm for this problem. We give optimal black hole search algorithms for two 'extreme' classes of trees: the class of lines and the class of trees in which any internal node (including the root which is the starting node) has at least two children.

AB - A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous tree network, assuming an upper bound on the time of any edge traversal by an agent. The minimum number of agents capable of identifying a black hole is two. For a given tree and given starting node we are interested in the fastest-possible black hole search by two agents. For arbitrary trees we give a 5/3-approximation algorithm for this problem. We give optimal black hole search algorithms for two 'extreme' classes of trees: the class of lines and the class of trees in which any internal node (including the root which is the starting node) has at least two children.

UR - http://www.scopus.com/inward/record.url?scp=34249980141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249980141&partnerID=8YFLogxK

U2 - 10.1017/S0963548306008133

DO - 10.1017/S0963548306008133

M3 - Article

AN - SCOPUS:34249980141

VL - 16

SP - 595

EP - 619

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 4

ER -