FPTAS's for some cut problems in weighted trees

Authors:
Mingyu Xiao;Takuro Fukunaga;Hiroshi Nagamochi
Affiliations:
School of Computer Science and Engineering, University of Electronic Science and Technology of China, China;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan
Venue:
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Year:
2010

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FPTASs for trimming weighted trees

Theoretical Computer Science

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Abstract

Given a tree with nonnegative edge cost and nonnegative vertex weight, and a number k ≥ 0, we consider the following four cut problems: cutting vertices of weight at most or at least k from the tree by deleting some edges such that the remaining part of the graph is still a tree and the total cost of the edges being deleted is minimized or maximized. The MinMstCut problem (cut vertices of weight at most k and minimize the total cost of the edges being deleted) can be solved in linear time and space and the other three problems are NP-hard. In this paper, we design an O(ln/ε)-time O(l2/ε + n)-space algorithm for MaxMstCut, and O(ln(1/ε + log n))-time O(l2/ε + n)-space algorithms for MinLstCut and MaxLstCut, where n is the number of vertices in the tree, l the number of leaves, and ε 0 the prescribed error bound.