An optimal time algorithm for finding a maximum weight independent set in a tree
Copyright policy )An optimal time algorithm for finding a maximum weight independent set in a tree
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.
dynamic programming, Graph theory (including graph drawing) in computer science, Analysis of algorithms and problem complexity, time optimal, Dynamic programming, maximum weight independent set in trees
dynamic programming, Graph theory (including graph drawing) in computer science, Analysis of algorithms and problem complexity, time optimal, Dynamic programming, maximum weight independent set in trees
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