On the characterization of the domination of a diameter-constrained network reliability model

Authors:
Héctor Cancela;Louis Petingi
Affiliations:
Departamento de Investigación Operativa, Instituto de Computación, Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay;Computer Science Department, College of Staten Island, City University of New York, IN, Staten Island, NY
Venue:
Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
Year:
2006

Citing 4
Cited 9

Network reliability and algebraic structures

Network reliability and algebraic structures
Approximating the weight of shallow Steiner trees

Discrete Applied Mathematics
A 2-path approach for odd-diameter-constrained minimum spanning and Steiner trees

Networks
Multicast routing with end-to-end delay and delay variation constraints

IEEE Journal on Selected Areas in Communications

Combinatorial and computational properties of a diameter constrained network reliability model

ACC'08 Proceedings of the WSEAS International Conference on Applied Computing Conference
A diameter-constrained network reliability model to determine the probability that a communication network meets delay constraints

WSEAS TRANSACTIONS on COMMUNICATIONS
Oriented matroid systems

Discrete Applied Mathematics
Reliability study of mesh networks modeled as random graphs

MMES'10 Proceedings of the 2010 international conference on Mathematical models for engineering science
New reliability model and its application to assess the performance of sensor networks

MMES'10 Proceedings of the 2010 international conference on Mathematical models for engineering science
Computing diameter constrained reliability of a network with junction points

Automation and Remote Control
Calculating two-terminal reliability in a diameter constrained network with cutnodes

Proceedings of the 6th International Conference on Ubiquitous Information Management and Communication
Monte Carlo estimation of diameter-constrained network reliability conditioned by pathsets and cutsets

Computer Communications
Decomposing graph with 2-node cuts for diameter constrained network reliability calculation

Proceedings of the 7th International Conference on Ubiquitous Information Management and Communication

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let G = (V, E) be a digraph with a distinguished set of terminal vertices K ⊆ V and a vertex s ∈ K. We define the s, K-diameter of G as the maximum distance between s and any of the vertices of K. If the arcs fail randomly and independently with known probabilities (vertices are always operational), the diameter-constrained s, K-terminal reliability of G, Rs,K(G, D), is defined as the probability that surviving arcs span a subgraph whose s, K-diameter does not exceed D.The diameter-constrained network reliability is a special case of coherent system models, where the domination invariant has played an important role, both theoretically and for developing algorithms for reliability computation. In this work, we completely characterize the domination of diameter-constrained network models, giving a simple rule for computing its value: if the digraph either has an irrelevant arc, includes a directed cycle or includes a dipath from s to a node in K longer than D, its domination is 0; otherwise, its domination is - 1 to the power |E| - |V| + 1. In particular this characterization yields the classical source-to-K-terminal reliability domination obtained by Satyanarayana.Based on these theoretical results, we present an algorithm for computing the reliability.