An optimal time algorithm for finding a maximum weight independent set in a tree (Q1107326)

The maximum weight independent set problem for a general graph is NP- hard. But for some special classes of graphs, polynomial time algorithms do exist for solving it. Based on the divide-and-conquer strategy, \textit{Sh. Pawagi} [ibid. 27, 170-180 (1987; Zbl 0642.68128)] has presented an O(\(| V| \log | V|)\) time algorithm for solving this problem on a tree. In this paper, we propose an O(\(| V|)\) time algorithm to improve Pawagi's result. The proposed algorithm is based on the dynamic programming strategy and is time optimal within a constant factor.