论文信息 - On random minimum length spanning trees

On random minimum length spanning trees

We extend and strengthen the result that, in the complete graphKn with independent random edge-lengths uniformly distributed on [0, 1], the expected length of the minimum spanning tree tends toζ(3) asn→∞. In particular, ifKn is replaced by the complete bipartite graphKn, n then there is a corresponding limit of 2ζ (3).

C. McDiarmid | A. Frieze

[1] M. Loève. On Almost Sure Convergence , 1951 .

[2] P. A. P. Moran,et al. An introduction to probability theory , 1968 .

[3] Alan M. Frieze,et al. On the value of a random minimum spanning tree problem , 1985, Discret. Appl. Math..

[4] Béla Bollobás,et al. On the expected behavior of disjoint set union algorithms , 1985, STOC '85.

[5] Colin McDiarmid. On the greedy algorithm with random costs , 1986, Math. Program..

[6] J. Michael Steele,et al. On Frieze's χ(3) limit for lengths of minimal spanning trees , 1987, Discret. Appl. Math..