Lazy listing of equivalence classes -- A paper on dynamic programming and tropical circuits

When a problem has more than one solution, it is often important, depending on the underlying context, to list them all. Even when the listing 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. This paper addresses this problem by proposing what we called a \emph{lazy listing} algorithm. By this we mean that, instead of listing all solutions, we list, in an efficient way, directly only the equivalence classes or one representative per class. Besides the need to then provide an \emph{a priori} relation of equivalence between solutions, we place ourselves in the special context where the problem to be addressed, either after some preliminary polynomial time dynamic programming computation or directly from the start, leads to a decomposable tropical circuit.