A network flow approach to cost allocation for rooted trees

Authors:
Satoru Iwata;Nozomu Zuiki
Affiliations:
Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan;Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
Venue:
Networks
Year:
2004

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Efficient solutions to relaxations of combinatorial problems with submodular penalties via the Lovász extension and non-smooth convex optimization

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms

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Abstract

In the game theory approach to cost allocation, the main computational issue is an algorithm for finding solutions such as the Shapley value and the nucleolus. In this article, we consider the problem of allocating the maintenance cost of a tree network that connects the supply source at the root to the users at the leaves. We show that the core of the game can be expressed in terms of network flows. Based on this observation, we present O(n log n) algorithms for computing the nucleolus and the egalitarian allocation. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(4), 297–301 2004