On the longest path algorithm for reconstructing trees from distance matrices

Culberson and Rudnicki [1] gave an algorithm that reconstructs a degree d restricted tree from its distance matrix. According to their analysis, it runs in time O(dn logd n) for topological trees. However, this turns out to be false; we show that the algorithm takes Θ(n3/2 √ d) time in the topological case, giving tight examples. Key words: Analysis of algorithms, graph algorithms

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Lev Reyzin, Nikhil Srivastava
• Keywords: Algorithms, Distance Matrix, IPL 2007, Topological Trees