ylfink@water.waterloo.edu (ylfink) (02/05/88)
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF WATERLOO SEMINAR ACTIVITIES ENUMERATIVE COMBINATORICS SEMINAR - Wednesday, February 10, 1988 Mr. Robert P.J. Day, a graduate student of this department, will speak on ``Unranking and Ranking Spanning Trees of a Graph''. TIME: 1:30 PM ROOM: MC 5158A ABSTRACT The set S of spanning trees of an n-vertex graph G can be placed in one-to-one correspondence with the integers in the interval [1,s], where s = |S|. We 3 develop O(n ) unranking and ranking functions for the spanning trees of an arbitrary graph. The unranking function maps any integer in the interval |1,s| to the corresponding tree, while the ranking function maps a spanning tree to the appropriate index in the interval. 3 The unranking function provides an O(n ) method for generating uniformly-distributed random spanning trees of a graph, a significant improvement over the more 5 3 straightforward and obvious O(n ) and O(n m) methods.