TY - JOUR

T1 - Bounds for All-Terminal Reliability in Planar Networks

AU - Ramesh, Aparna

AU - Ball, Michael O.

AU - Colbourn, Charles J.

N1 - Funding Information:
Research of the second author is supported by the U.S. Army Research Office. Research of the third author is supported by NSERC Canada under grant A0579.

PY - 1987/1

Y1 - 1987/1

N2 - A communication network can be modeled as a graph where the nodes of the graph represent the sites, and the edges represent the links between the sites. The edges of the graph operate with equal probability p. The all-terminal reliability of the network with n nodes and b edges can be written as where Fiis the number of connected subgraphs with (b - i) edges and q= (1 -p). All known subgraph counting bounds for R use exact values for F0, …, Fcand Fdwhere c is the cardinality of a minimum cut and d=b - n + 1. In this paper we derive upper and lower bounds for R for planar networks by using exact values of Fd-1, Fd-2, Fd-3, Fc+1and Fc+2where approximations were used before. The effect of using these exact values instead of approximations on Kruskal-Katona bounds and Ball-Provan bounds is studied.

AB - A communication network can be modeled as a graph where the nodes of the graph represent the sites, and the edges represent the links between the sites. The edges of the graph operate with equal probability p. The all-terminal reliability of the network with n nodes and b edges can be written as where Fiis the number of connected subgraphs with (b - i) edges and q= (1 -p). All known subgraph counting bounds for R use exact values for F0, …, Fcand Fdwhere c is the cardinality of a minimum cut and d=b - n + 1. In this paper we derive upper and lower bounds for R for planar networks by using exact values of Fd-1, Fd-2, Fd-3, Fc+1and Fc+2where approximations were used before. The effect of using these exact values instead of approximations on Kruskal-Katona bounds and Ball-Provan bounds is studied.

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U2 - 10.1016/S0304-0208(08)73060-3

DO - 10.1016/S0304-0208(08)73060-3

M3 - Article

AN - SCOPUS:77956902585

VL - 144

SP - 261

EP - 273

JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

SN - 0304-0208

IS - C

ER -