Optimum requirement spanning trees and reliability of tree networks

Anazawa, Tsutomu; Kodera, Takayuki; Jimbo, Masakazu

doi:10.1002/(sici)1097-0037(199909)34:2<122::aid-net5>3.0.co;2-p

Cited by 3 publications

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References 2 publications

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“…This procedure can be regarded as a sort of greedy algorithm. The condition for T Ã to minimize f subject to (1) was relaxed by Anazawa et al (1999) and Anazawa (1999). Anazawa et al (1999) showed that T Ã is optimum even in the case of p 0 > p 1 > Á Á Á > p nÀ1 .…”

Section: Introductionmentioning

confidence: 99%

An Explicit Solution of a Generalized Optimum Requirement Spanning Tree Problem With a Property Related to Monge

Anazawa

2001

Int Trans Operational Res

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The paper considers a generalization of the optimum requirement spanning tree problem (ORST problem) ®rst studied by Hu in 1974. Originally, ORST was regarded as a communication network of tree type with the minimum average cost, and it is obtained by the well-known Gomory±Hu algorithm when the degrees of vertices are not restricted. The ORST problem is generalized by (i) generalizing the objective function and (ii) imposing maximum degree constraints. The generalized ORST problem includes some practical problems, one of which is proposed in this paper, but is not ef®ciently solvable in general. However, I show that a particular tree (which is obtained by a sort of greedy algorithm but is explicitly de®nable) is a solution of the generalized problem when a certain practical condition is satis®ed. The condition is closely related to the Monge property, which is originally discussed in the Hitchcock transportation problem, and is known to make some NP-hard problems ef®ciently solvable.

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Section: Introductionmentioning

confidence: 99%

An Explicit Solution of a Generalized Optimum Requirement Spanning Tree Problem With a Property Related to Monge

Anazawa

2001

Int Trans Operational Res

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Network reliability: Heading out on the highway

et al. 2020

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A variety of probabilistic notions of network reliability of graphs and digraphs have been proposed and studied since the early 1950s. Although grounded in the engineering and logistics of network design and analysis, the research also spans pure and applied mathematics, with connections to areas as diverse as combinatorics and graph theory, combinatorial enumeration, optimization, probability theory, real and complex analysis, algebraic topology, commutative algebra, the design and analysis of algorithms, and computational complexity. In this paper we describe the landscape of various notions of network reliability, the roads well traveled, and some that appear likely to lead to meaningful and important journeys.

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A Generalized Optimum Requirement Spanning Tree Problem With a Monge-Like Property

Anazawa

2000

JORSJ

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Optimum requirement spanning trees and reliability of tree networks

Cited by 3 publications

References 2 publications

An Explicit Solution of a Generalized Optimum Requirement Spanning Tree Problem With a Property Related to Monge

An Explicit Solution of a Generalized Optimum Requirement Spanning Tree Problem With a Property Related to Monge

Network reliability: Heading out on the highway

A Generalized Optimum Requirement Spanning Tree Problem With a Monge-Like Property

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