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Diameter-Constrained Reliability: Complexity, Factorization and Exact computation in Weak Graphs

Authors:

Eduardo Canale,

Franco Robledo,

Pablo RomeroAuthors Info & Claims

LANC '14: Proceedings of the Latin America Networking Conference on LANC 2014

Article No.: 12, Pages 1 - 7

https://doi.org/10.1145/2684083.2684095

Published: 18 September 2014 Publication History

Abstract

In this paper we address a problem from the field of network reliability, called diameter-constrained reliability. Specifically, we are given a simple graph G = (V, E) with [V] = n nodes and [E] = m links, a subset K ⊆ V of terminals, a vector p = (p1,...,pm) ϵ [0, 1]m and a positive integer d, called diameter. We assume nodes are perfect but links fail stochastically and independently, with probabilities qi = 1 --- pi. The diameter-constrained reliability (DCR for short), is the probability that the terminals of the resulting subgraph remain connected by paths composed by d links, or less. This number is denoted by RdK,G(p).

The general DCR computation is inside the class of NP-Hard problems, since is subsumes the complexity that a random graph is connected. In this paper the computational complexity of DCR-subproblems is discussed in terms of the number of terminal nodes k = [K] and diameter d. A factorization formula for exact DCR computation is provided, that runs in exponential time in the worst case. Finally, a revision of graph-classes that accept DCR computation in polynomial time is then included. In this class we have graphs with bounded co-rank, graphs with bounded genus, planar graphs, and, in particular, Monma graphs, which are relevant in robust network design. We extend this class adding arborescence graphs. A discussion of trends for future work is offered in the conclusions.

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Cited By

Canale ERobledo FRomero PViera J(2019)Building Reliability-Improving Network Transformations2019 15th International Conference on the Design of Reliable Communication Networks (DRCN)10.1109/DRCN.2019.8713759(107-113)Online publication date: Mar-2019
https://doi.org/10.1109/DRCN.2019.8713759
Canale ERobledo FRomero PSartor P(2018)Monte Carlo methods in diameter-constrained reliabilityOptical Switching and Networking10.1016/j.osn.2014.06.00314(134-148)Online publication date: 20-Dec-2018
https://dl.acm.org/doi/10.1016/j.osn.2014.06.003
Romero P(2017)Building uniformly most-reliable networks by iterative augmentation2017 9th International Workshop on Resilient Networks Design and Modeling (RNDM)10.1109/RNDM.2017.8093016(1-7)Online publication date: Sep-2017
https://doi.org/10.1109/RNDM.2017.8093016
Show More Cited By

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Diameter-Constrained Reliability: Complexity, Factorization and Exact computation in Weak Graphs

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cover image ACM Other conferences

LANC '14: Proceedings of the Latin America Networking Conference on LANC 2014

September 2014

91 pages

ISBN:9781450332804

DOI:10.1145/2684083

General Chair:
Eduardo Cerqueira
Federal University of Para, BR

Copyright © 2014 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 18 September 2014

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LANC '14: Latin America Networking Conference

September 18 - 19, 2014

Montevideo, Uruguay

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Cited By

Canale ERobledo FRomero PViera J(2019)Building Reliability-Improving Network Transformations2019 15th International Conference on the Design of Reliable Communication Networks (DRCN)10.1109/DRCN.2019.8713759(107-113)Online publication date: Mar-2019
https://doi.org/10.1109/DRCN.2019.8713759
Canale ERobledo FRomero PSartor P(2018)Monte Carlo methods in diameter-constrained reliabilityOptical Switching and Networking10.1016/j.osn.2014.06.00314(134-148)Online publication date: 20-Dec-2018
https://dl.acm.org/doi/10.1016/j.osn.2014.06.003
Romero P(2017)Building uniformly most-reliable networks by iterative augmentation2017 9th International Workshop on Resilient Networks Design and Modeling (RNDM)10.1109/RNDM.2017.8093016(1-7)Online publication date: Sep-2017
https://doi.org/10.1109/RNDM.2017.8093016
Rela GRobledo FRomero P(2017)Petersen Graph is Uniformly Most-ReliableMachine Learning, Optimization, and Big Data10.1007/978-3-319-72926-8_35(426-435)Online publication date: 21-Dec-2017
https://doi.org/10.1007/978-3-319-72926-8_35
Romero P(2016)Duality in stochastic binary systems2016 8th International Workshop on Resilient Networks Design and Modeling (RNDM)10.1109/RNDM.2016.7608272(85-91)Online publication date: Sep-2016
https://doi.org/10.1109/RNDM.2016.7608272

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