Complexity of inheritance of F-convexity for restricted games induced by minimum partitionsReport as inadecuate




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* Corresponding author 1 CES - Centre d-économie de la Sorbonne

Abstract : Let G = N,E,w be a weighted communication graph with weight function w on E . For every subset A ⊆ N, we delete in the subset E A of edges with ends in A, all edges of minimum weight in E A . Then the connected components of the corresponding induced subgraph constitue a partition of A that we PminA . For every game N , v , we define the Pmin-restricted game N , v by v A = ∑F∈ Pmin A vF for all A ⊆ N. We prove that we can decide in polynomial time if there is inheritance of F-convexity from N , v to the Pmin-restricted game N , v where F-convexity is obtained by restricting convexity to connected subsets

Keywords : restricted game convex game cooperative game communication networks partitions supermodularity complexity graph





Author: Alexandre Skoda -

Source: https://hal.archives-ouvertes.fr/



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