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SODA
2004
ACM

Covering minimum spanning trees of random subgraphs

9 years 5 months ago
Covering minimum spanning trees of random subgraphs
We consider the problem of finding a sparse set of edges containing the minimum spanning tree (MST) of a random subgraph of G with high probability. The two random models that we consider are subgraphs induced by a random subset of vertices, each vertex included independently with probability p, and subgraphs generated as a random subset of edges, each edge with probability p. Let n denote the number of vertices, choose p (0, 1) possibly depending on n and let b = 1/(1 - p). We show that in both random models, for any weighted graph G, there is a set of edges Q of cardinality O(n logb n) which contains the minimum spanning tree of a random subgraph of G with high probability. This result is asymptotically optimal. As a consequence, we also give a bound of O(kn) on the size of the union of all minimum spanning trees of G with some k vertices (or edges) removed. More generally, we show a bound of O(n logb n) on the size of a covering set in a matroid of rank n, which contains the minim...
Michel X. Goemans, Jan Vondrák
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2004
Where SODA
Authors Michel X. Goemans, Jan Vondrák
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