Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Generating all vertices of a polyhedron is hard
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Multicriteria Optimization
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WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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SAGA'05 Proceedings of the Third international conference on StochasticAlgorithms: foundations and applications
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Journal of Experimental Algorithmics (JEA)
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We propose a polynomial-time-delay polynomial-space algorithm to enumerate all efficient extreme solutions of a multicriteria 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 polynomialtime delay and polynomial-space algorithms for the problems.