A Polynomial-Time-Delay and Polynomial-Space Algorithm for Enumeration Problems in Multi-criteria Optimization

  • Yoshio Okamoto
  • Takeaki Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4835)


We propose a polynomial-time-delay polynomial-space algorithm to enumerate all efficient extreme solutions of a multi-criteria minimum-cost spanning tree problem, while only the bi-criteria case was studied in the literature. The algorithm is based on the reverse search framework due to Avis & Fukuda. We also show that the same technique can be applied to the multi-criteria version of the minimum-cost basis problem in a (possibly degenerated) submodular system. As an ultimate generalization, we propose an algorithm to enumerate all efficient extreme solutions of a multi-criteria linear program. When the given linear program has no degeneracy, the algorithm runs in polynomial-time delay and polynomial space. To best of our knowledge, they are the first polynomial-time delay and polynomial-space algorithms for the problems.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yoshio Okamoto
    • 1
  • Takeaki Uno
    • 2
  1. 1.Department of Information and Computer Sciences, Toyohashi University of Technlology, Hibarigaoka 1–1, Tempaku, Toyohashi, Aichi, 441-8580Japan
  2. 2.National Institute of Informatics, Hitotsubashi 2–1–2, Chiyoda-ku, Tokyo, 101-8430Japan

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