Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Resource-Based Fitness Sharing
PPSN VII Proceedings of the 7th International Conference on Parallel Problem Solving from Nature
Shape nesting by coevolving species
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Optimal nesting of species for exact cover of resources: two against many
Proceedings of the 9th annual conference on Genetic and evolutionary computation
NP-completeness and the coevolution of exact set covers
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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Experiments with resource-defined fitness sharing (RFS) applied to shape nesting problems indicate a remarkable ability to discover exact covers of resources [1, 2]. These exact covers are represented by a maximally sized set of cooperating (non-competing) species. Recent papers by Horn [3, 4] introduce the first formal analyses of this empirical phenomenon. In [3], a minimal case of two species, aand b, against a third, c, is considered: the two-against-onescenario. It is shown that if the team of aand bform an exact cover, then cwill be extinct at niching equilibrium. In [4], this result is generalized to the case of two-against-many: if aand bform an exact cover against an arbitrary number of competing species, under very general assumptions, aand bwill be the only survivors at niching equilibirum. In the current paper, we extend these results to the most general scenario: many-against-many. We prove that, under certain very general assumptions, any size team of species forming an exact cover will dominate a population with any number of competing species: at niching equilibirum, all such competitors will be extinct. The results are more general than shape-nesting problems, applying as well to the NP-complete problem exact cover by k-sets.