We present an algorithm for counting the number of minimum weight spanning trees, based on the fact that the generating function for the number of spanning trees of a given graph, by weight, can be expressed as a simple determinant. For a graph with n vertices and m edges, our Ε½ Ε½ .. Ε½ . algorithm r
Minimum-weight two-connected spanning networks
β Scribed by Clyde L. Monma; Beth Spellman Munson; William R. Pulleyblank
- Publisher
- Springer-Verlag
- Year
- 1990
- Tongue
- English
- Weight
- 984 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0025-5610
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We investigate Prim's standard ''tree-growing'' method for finding a minimum spanning tree, when applied to a network in which all degrees are about d and the edges e Ε½ . have independent identically distributed random weights w e . We find that when the kth ' Ε½ . edge e is added to the current tree
## Abstract In this paper, we propose the problem of identifying a minimumβweight rooted notβnecessarilyβspanning arborescence (MRA) in a directed rooted acyclic graph with weights on arcs. We show this problem to be NPβhard and formulate it as a zeroβone integer program. We develop a heuristic __H