Given a tree \documentclass[12pt]{minimal}
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\begin{document}$$T = (V, E)$$\end{document} with \documentclass[12pt]{minimal}
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\begin{document}$$n$$\end{document} vertices and a collection of terminal sets \documentclass[12pt]{minimal}
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\begin{document}$$D = \{S_1, S_2, \ldots , S_c\}$$\end{document}, where each \documentclass[12pt]{minimal}
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\begin{document}$$S_i$$\end{document} is a subset of \documentclass[12pt]{minimal}
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\begin{document}$$V$$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$$c$$\end{document} is a constant, the generalized multiway cut in trees problem (GMWC(T)) asks to find a minimum size edge subset \documentclass[12pt]{minimal}
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\begin{document}$$E^{\prime } \subseteq E$$\end{document} such that its removal from the tree separates all terminals in \documentclass[12pt]{minimal}
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\begin{document}$$S_i$$\end{document} from each other for each terminal set \documentclass[12pt]{minimal}
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\begin{document}$$S_i$$\end{document}. The GMWC(T) problem is a natural generalization of the classical multiway cut in trees problem, and has an implicit relation to the Densest \documentclass[12pt]{minimal}
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\begin{document}$$k$$\end{document}-Subgraph problem. In this paper, we show that the GMWC(T) problem is fixed-parameter tractable by giving an \documentclass[12pt]{minimal}
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\begin{document}$$O(n^2 + 2^k)$$\end{document} time algorithm, where \documentclass[12pt]{minimal}
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\begin{document}$$k$$\end{document} is the size of an optimal solution, and the GMWC(T) problem is polynomial time solvable when the problem is restricted in paths.We also discuss some heuristics for the GMWC(T) problem
