A depth-first dynamic programming algorithm for the Tree Knapsack Problem

A depth-first dynamic programming algorithm for the Tree Knapsack Problem

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Article ID: iaor1999400
Country: United States
Volume: 9
Issue: 4
Start Page Number: 431
End Page Number: 438
Publication Date: Sep 1997
Journal: INFORMS Journal On Computing
Authors: ,
Keywords: networks, graphs
Abstract:

The Tree Knapsack Problem (TKP) can be regarded as a 0–1 knapsack problem on a rooted tree T such that if a node is selected into a knapsack, then all nodes on the path from the selected node to the root node must also be selected into the knapsack. In this paper, we develop a pseudopolynomial-time algorithm for TKP, the depth-first dynamic programming algorithm. We prove that a TKP can be solved by our algorithm in θ(nH) time, where n is the number of nodes in T and H is the given capacity. We also report the computational results of the depth-first dynamic programming algorithm.

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