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2014•RePEc: Research Papers in EconomicsRequires access

It is hard to agree on a spanning tree

Andreas Darmann

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Abstract

We consider the problem of finding a "fair" or "acceptable" spanning tree in an undirected graph when each member of a group of agents proposes a spanning tree. An "acceptable" spanning tree in that respect is a spanning tree which does not differ in more than a given number of edges from each of the single proposals. We show that, from a computational perspective, determining if such a spanning tree exists is a difficult (NP-complete) problem.

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We consider the problem of finding a "fair" or "acceptable" spanning tree in an undirected graph when each member of a group of agents proposes a spanning tree. An "acceptable" spanning tree in that respect is a spanning tree which does not differ in more than a given number of edges from each of the single proposals. We show that, from a computational perspective, determining if such a spanning tree exists is a difficult (NP-complete) problem.

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Available abstract

We consider the problem of finding a "fair" or "acceptable" spanning tree in an undirected graph when each member of a group of agents proposes a spanning tree. An "acceptable" spanning tree in that respect is a spanning tree which does not differ in more than a given number of edges from each of the single proposals. We show that, from a computational perspective, determining if such a spanning tree exists is a difficult (NP-complete) problem.

Key concepts: Spanning tree, Distributed minimum spanning tree, Minimum spanning tree, k-minimum spanning tree, Connected dominating set, Combinatorics, Minimum degree spanning tree, Euclidean minimum spanning tree

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