Amortized efficiency of constructing multiple independent spanning trees on bubble-sort networks

Shih Shun Kao, Kung Jui Pai, Sun-Yuan Hsieh, Ro Yu Wu, Jou Ming Chang

Research output: Contribution to journalArticle

Abstract

A set of spanning trees in a graph G is called independent spanning trees (ISTs for short) if they are rooted at the same vertex, say r, and for each vertex v(≠ r) in G, the two paths from v to r in any two trees share no common edge and no common vertex except for v and r. Constructing ISTs has applications on fault-tolerant broadcasting and secure message distribution in reliable communication networks. Since Cayley graphs have been used extensively to design the topologies of interconnection networks, construction of ISTs on Cayley graphs is significative. It is well-known that star networks Sn and bubble-sort network Bn are two of the most attractive subclasses of Cayley graphs. Although it has been dealt with about two decades for the construction of ISTs on Sn (which has been pointed out that there is a flaw and has been corrected recently), so far the problem of constructing ISTs on Bn is not dealt with yet. In this paper, we present an algorithm to construct n- 1 ISTs of Bn. Moreover, we show that our algorithm has amortized efficiency for multiple trees construction. In particular, every vertex can determine its parent in each spanning tree in a constant amortized time. Accordingly, except for the star networks, it seems that our work is the latest breakthrough on the problem of ISTs for all subfamilies of Cayley graphs.

Original languageEnglish
Pages (from-to)972-986
Number of pages15
JournalJournal of Combinatorial Optimization
Volume38
Issue number3
DOIs
Publication statusPublished - 2019 Oct 15

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Bubble sort
Cayley Graph
Spanning tree
Stars
Vertex of a graph
Star
Broadcasting
Telecommunication networks
Interconnection Networks
Time Constant
Fault-tolerant
Topology
Communication Networks
Defects
Path
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Kao, Shih Shun ; Pai, Kung Jui ; Hsieh, Sun-Yuan ; Wu, Ro Yu ; Chang, Jou Ming. / Amortized efficiency of constructing multiple independent spanning trees on bubble-sort networks. In: Journal of Combinatorial Optimization. 2019 ; Vol. 38, No. 3. pp. 972-986.
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Amortized efficiency of constructing multiple independent spanning trees on bubble-sort networks. / Kao, Shih Shun; Pai, Kung Jui; Hsieh, Sun-Yuan; Wu, Ro Yu; Chang, Jou Ming.

In: Journal of Combinatorial Optimization, Vol. 38, No. 3, 15.10.2019, p. 972-986.

Research output: Contribution to journalArticle

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