Recent trends in hierarchic document clustering: a critical review
Information Processing and Management: an International Journal
A heuristic with worst-case analysis for minimax routing of two travelling salesmen on a tree
Discrete Applied Mathematics
(p-1)/(p+1)-approximate algorithms for p-traveling salemen problems on a tree with minmax objective
Discrete Applied Mathematics
On the merits of building categorization systems by supervised clustering
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
A Shifting Algorithm for Min-Max Tree Partitioning
Journal of the ACM (JACM)
Tree partitioning under constraints - clustering for vehicle routing problems
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Aspects of edge list-colourings
Discrete Mathematics - Special issue on the 17th british combinatorial conference selected papers
Introduction to Algorithms
XRules: an effective structural classifier for XML data
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
On the complexity of graph tree partition problems
Discrete Applied Mathematics
Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters
IEEE Transactions on Computers
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Given a tree of n vertices and a list of feasible colours for each vertex, the coloured tree partition problem (CTPP) consists in partitioning the tree into p vertex-disjoint subtrees of minimum total cost, and assigning to each subtree a different colour, which must be feasible for all of its vertices. The problem is strongly NP-hard on general graphs, as well as on grid and bipartite graphs. This paper deals with the previously open case of tree graphs, showing that it is strongly NP-complete to determine whether a feasible solution exists. It presents reduction, decomposition and bounding procedures to simplify the problem and an exact algorithm of O(np^l^o^g^"^2^(^a^p^-^2^)) complexity (with a32) for the special case in which a vertex of each subtree is given.