Finding good approximate vertex and edge partitions is NP-hard
Information Processing Letters
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Computers and Operations Research
On cutting a few vertices from a graph
Discrete Applied Mathematics
Simplifying decision trees: A survey
The Knowledge Engineering Review
Finding small balanced separators
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Algorithmica - Special Issue: Algorithms and Computation; Guest Editor: Takeshi Tokuyama
FPTAS's for some cut problems in weighted trees
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
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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 mostk 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(nl/@e)-time O(l^2/@e+n)-space algorithm for MaxMstCut, and O(nl(1/@e+logn))-time O(l^2/@e+n)-space algorithms for the other two problems, MinLstCut and MaxLstCut, where n is the number of vertices in the tree, l the number of leaves, and @e0 the prescribed error bound.