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A problem of network stability.

Walsh, Matthew Philip.

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A problem of network stability.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	A problem of network stability./
作者:	Walsh, Matthew Philip.
面頁冊數:	47 p.
附註:	Director: Peter D. Johnson, Jr.
Contained By:	Dissertation Abstracts International63-02B.
標題:	Computer Science. -
電子資源:	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.
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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.
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650 4 $a Engineering, System Science. $3 1018128
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791 $a Ph.D.
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