# Minimum cost partitions of trees with supply and demand

Takehiro Ito, Takuya Hara, Xiao Zhou, Takao Nishizeki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

## Abstract

Let T be a given tree. Each vertex of T is either a supply vertex or a demand vertex, and is assigned a positive integer, called the supply or the demand. Every demand vertex v of T must be supplied an amount of "power," equal to the demand of v, from exactly one supply vertex through edges in T. Each edge e of T has a direction, and is assigned a positive integer which represents the cost required to delete e from T or reverse the direction of e. Then one wishes to obtain subtrees of T by deleting edges and reversing the directions of edges so that (a) each subtree contains exactly one supply vertex whose supply is no less than the sum of all demands in the subtree and (b) each subtree is rooted at the supply vertex in a sense that every edge is directed away from the root. We wish to minimize the total cost to obtain such rooted subtrees from T. In the paper, we first show that this minimization problem is NP-hard, and then give a pseudo-polynomial-time algorithm to solve the problem. We finally give a fully polynomial-time approximation scheme (FPTAS) for the problem.

Original language English Algorithms and Computation - 21st International Symposium, ISAAC 2010, Proceedings 351-362 12 PART 2 https://doi.org/10.1007/978-3-642-17514-5_30 Published - 2010 21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 - Jeju Island, Korea, Republic ofDuration: 2010 Dec 15 → 2010 Dec 17

### Publication series

Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) PART 2 6507 LNCS 0302-9743 1611-3349

### Other

Other 21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 Korea, Republic of Jeju Island 10/12/15 → 10/12/17

## ASJC Scopus subject areas

• Theoretical Computer Science
• Computer Science(all)

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