A divide-and-conquer algorithm for finding a most reliable source on a ring-embedded tree network with unreliable edges

W. E.I. Ding, Guoliang Xue

Research output: Contribution to journalArticle

Abstract

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 an MRS, and employ a binary division tree (BDT) to analyze its time complexity to be O(||λ||2/2+[log|λ|] ||λ||1).

Original languageEnglish (US)
Pages (from-to)503-516
Number of pages14
JournalDiscrete Mathematics, Algorithms and Applications
Volume3
Issue number4
DOIs
StatePublished - Dec 1 2011

Fingerprint

Divide-and-conquer Algorithm
Ring Network
Tree Networks
Ring
Tolerance
Topology
Computing
Divide and conquer
Graph in graph theory
Vertex of a graph
Communication Networks
Fast Algorithm
Time Complexity
Strip
Linear Time
Division
Maximise
Binary
Class

Keywords

  • Divide-and-Conquer algorithm
  • Most reliable source
  • ring-tree
  • underlying topology

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

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