Fast Algorithms for Constructing Maximum Entropy Summary Trees

Richard Cole, Howard J. Karloff

Abstract: Karloff and Shirley recently proposed “summary trees” as a new way to visualize large rooted trees (Eurovis 2013) and gave algorithms for generating a maximum-entropy k-node summary tree of an input n-node rooted tree. However, the algorithm generating optimal summary trees was only pseudo-polynomial (and worked only for integral weights); the authors left open existence of a polynomial-time algorithm. In addition, the authors provided an additive approximation algorithm and a greedy heuristic, both working on real weights.