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A General Framework for Enumerating Equivalence Classes of Solutions

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Abstract

When a problem has more than one solution, it is often important, depending on the underlying context, to enumerate (i.e., to list) them all. Even when the enumeration can be done in polynomial delay, that is, spending no more than polynomial time to go from one solution to the next, this can be costly as the number of solutions themselves may be huge, including sometimes exponential. Furthermore, depending on the application, many of these solutions can be considered equivalent. The problem of an efficient enumeration of the equivalence classes or of one representative per class (without generating all the solutions), although identified as a need in many areas, has been addressed only for very few specific cases. In this paper, we provide a general framework that solves this problem in polynomial delay for a wide variety of optimization problems solvable by dynamic programming algorithms, and for certain types of equivalence relations between solutions.

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Authors and Affiliations

  1. CNRS, Laboratoire de Biométrie et Biologie Evolutive UMR 5558, Université de Lyon, Université Lyon 1, Villeurbanne, 69622, France

    Yishu Wang, Arnaud Mary & Marie-France Sagot

  2. Inria Lyon, Villeurbanne, France

    Yishu Wang, Arnaud Mary & Marie-France Sagot

  3. Luiss University, Rome, Italy

    Blerina Sinaimeri

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  1. Yishu Wang
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  3. Marie-France Sagot
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Wang, Y., Mary, A., Sagot, MF. et al. A General Framework for Enumerating Equivalence Classes of Solutions. Algorithmica 85, 3003–3023 (2023). https://doi.org/10.1007/s00453-023-01131-1

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