Linking and Cutting Spanning Trees

Abstract

Abstract:We consider the problem of uniformly generating a spanning tree for an undirected connected graph. This process is useful for computing statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle graphs, we prove that this approach significantly outperforms existing algorithms. For general graphs, experimental results show that the chain converges quickly. This yields an efficient algorithm due to the use of proper fast data structures. To obtain the mixing time of the chain we describe a coupling, which we analyze for cycle graphs and simulate for other graphs.

Editorial: Special Issue on Efficient Data Structures

“…After several rounds of revisions and reviewing, six of the submitted articles were accepted for inclusion in the Special Issue. These six articles present new results for a wide variety of data structures with unexpectedly diverse applications: the link-cut tree (Russo et al [1]), the distributed combinatorial map (Damiand et al [2]), the sliding suffix tree (Brodnik and Jekovec [3]), the DenseZDD (Denzumi et al [4]), the dynamic DFS tree (Nakamura and Sadakane [5]), and the selectable sloppy heap (Dumitrescu [6]). As a whole, they represent some of the current trends in the field.…”