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Profile minimization on compositions of graphs

Author

Listed:
  • Yu-Ping Tsao

    (China University of Technology
    National Chiao Tung University)

  • Gerard J. Chang

    (National Taiwan University
    National Taiwan University
    National Center for Theoretical Sciences, Taipei Office)

Abstract

The profile minimization problem arose from the study of sparse matrix technique. In terms of graphs, the problem is to determine the profile of a graph G which is defined as $$P(G)=\min\limits_{f}\sum\limits_{v\in V(G)}\max\limits_{x\in N[v]}(f(v)-f(x)),$$ where f runs over all bijections from V(G) to {1,2,…,|V(G)|} and N[v]={v}∪{x∈V(G):xv∈E(G)}. This is equivalent to the interval graph completion problem, which is to find a super-graph of a graph G with as few number of edges as possible. The purpose of this paper is to study the profiles of compositions of two graphs.

Suggested Citation

  • Yu-Ping Tsao & Gerard J. Chang, 2007. "Profile minimization on compositions of graphs," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 177-190, October.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:2:d:10.1007_s10878-007-9061-9
    DOI: 10.1007/s10878-007-9061-9
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