Network reliability and algebraic structures
Network reliability and algebraic structures
Communication complexity for parallel divide-and-conquer
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A reliability model applied to emergency service vehicle location
Operations Research
Theoretical Computer Science
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
Graph Theory With Applications
Graph Theory With Applications
Computing the Most Reliable Source on Stochastic Ring Networks
WCSE '09 Proceedings of the 2009 WRI World Congress on Software Engineering - Volume 01
A linear time algorithm for computing a most reliable source on a tree network with faulty nodes
Theoretical Computer Science
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
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Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graphs is #P-hard. However, this problem in tree networks has been solved in a linear time. A tree network has a weakness of low capability of failure tolerance. Embedding rings into it by adding some additional certain edges to it can enhance its failure tolerance, resulting in another class of sparse networks, called the ring-tree networks. This class of network also has an underlying tree-like topology, leading to its advantage of being easily administrated. This paper concerns with an important case whose underlying topology is a strip graph, called λ-rings network, and focuses on an unreliable λ-rings network where each link has an independent operational probability while all nodes are immune to failures. We apply the Divide-and-Conquer approach to design a fast algorithm for computing its an MRS, and employ a binary division tree (BDT) to analyze its time complexity to be O(∥λ∥22+ ⌈log|λ|⌉ ċ ∥λ∥1).