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A problem of network stability.

Walsh, Matthew Philip.

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A problem of network stability.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	A problem of network stability./
Author:	Walsh, Matthew Philip.
Description:	47 p.
Notes:	Director: Peter D. Johnson, Jr.
Contained By:	Dissertation Abstracts International63-02B.
Subject:	Computer Science. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3044030
ISBN:	0493577289

A problem of network stability.
Walsh, Matthew Philip.

A problem of network stability. - 47 p.

Director: Peter D. Johnson, Jr.

Thesis (Ph.D.)--Auburn University, 2002.

Consider a graph <italic>G</italic> with a non-negative weight function <italic>w</italic> on its nodes. The nodes of this network are unstable in the following sense: a vertex bearing weight <italic>w</italic> will fail (and be deleted from the network) with probability <italic>f</italic>(<italic> w</italic>) for some known monotonic function <italic>f</italic>. After each vertex has been put to the test, we desire there to be a component of the remaining graph with its vertex weights summing to at least some value <italic> t</italic>; if this happens, we will say that the network <italic>survived </italic>. The <italic>network stability problem</italic> is to determine a weight function which will maximise the probability of survival.

ISBN: 0493577289Subjects--Topical Terms:

626642
Computer Science.

A problem of network stability.
LDR:02343nam 2200313 a 45 001 933683
005 20110506
008 110506s2002 eng d
020 $a 0493577289
035 $a (UnM)AAI3044030
035 $a AAI3044030
040 $a UnM $c UnM
100 1 $a Walsh, Matthew Philip. $3 1257418
245 1 0 $a A problem of network stability.
300 $a 47 p.
500 $a Director: Peter D. Johnson, Jr.
500 $a Source: Dissertation Abstracts International, Volume: 63-02, Section: B, page: 0834.
502 $a Thesis (Ph.D.)--Auburn University, 2002.
520 $a Consider a graph <italic>G</italic> with a non-negative weight function <italic>w</italic> on its nodes. The nodes of this network are unstable in the following sense: a vertex bearing weight <italic>w</italic> will fail (and be deleted from the network) with probability <italic>f</italic>(<italic> w</italic>) for some known monotonic function <italic>f</italic>. After each vertex has been put to the test, we desire there to be a component of the remaining graph with its vertex weights summing to at least some value <italic> t</italic>; if this happens, we will say that the network <italic>survived </italic>. The <italic>network stability problem</italic> is to determine a weight function which will maximise the probability of survival.
520 $a In this work we perform some preliminary investigations of the network stability problem, establishing that the desired weighting actually exists in certain natural cases and remarking on the structure of the solution space; while this does not actually lead to an algorithmic approach, it does suggest the path that one might take in search of a heuristic solution.
520 $a We will also discuss a “discrete” version of the problem, in which all vertex weights are equal. We bring to the analysis of this special case some new graph-theoretic tools: a generalisation of dependent sets of vertices; an analogue of edge-contraction for vertices; and a new measure of density of connectivity of a graph.
590 $a School code: 0012.
650 4 $a Computer Science. $3 626642
650 4 $a Engineering, System Science. $3 1018128
650 4 $a Mathematics. $3 515831
690 $a 0405
690 $a 0790
690 $a 0984
710 2 0 $a Auburn University. $3 1020457
773 0 $t Dissertation Abstracts International $g 63-02B.
790 $a 0012
790 1 0 $a Johnson, Peter D., Jr., $e advisor
791 $a Ph.D.
792 $a 2002
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3044030