A dynamic programming algorithm for tree-like weighted set packing problem

Authors:
Mehmet Gulek;Ismail Hakki Toroslu
Affiliations:
Middle East Technical University, Department of Computer Engineering, Ankara, Turkey;Middle East Technical University, Department of Computer Engineering, Ankara, Turkey
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

In hierarchical organizations, hierarchical structures naturally correspond to nested sets. That is, we have a collection of sets such that for any two sets, either one of them is a subset of the other, or they are disjoint. In other words, a nested set system forms a hierarchy in the form of a tree structure. The task assignment problem on such hierarchical organizations is a real life problem. In this paper, we introduce the tree-like weighted set packing problem, which is a weighted set packing problem restricted to sets forming tree-like hierarchical structure. We propose a dynamic programming algorithm with cubic time complexity.