Heuristics with constant error guarantees for the design of tree networks
Management Science
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Approximation algorithms for min-max tree partition
Journal of Algorithms
Approximation algorithms for minimum tree partition
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A class of heuristics for the constrained forest problem
Discrete Applied Mathematics
A subexponential algorithm for the coloured tree partition problem
Discrete Applied Mathematics
Minmax Tree Cover in the Euclidean Space
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Communication: A class of heuristics for the constrained forest problem
Discrete Applied Mathematics
32-approximation algorithm for two variants of a 2-depot Hamiltonian path problem
Operations Research Letters
Another greedy heuristic for the constrained forest problem
Operations Research Letters
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This paper concerns the optimal partition of a graph into p connected clusters of vertices, with various constraints on their topology and weight. We consider different objectives, depending on the cost of the trees spanning the clusters. This rich family of problems mainly applies to telecommunication network design, but it can be useful in other fields. We achieve a complete characterization of its computational complexity, previously studied only for special cases: a polynomial algorithm based on a new matroid solves the easy cases; the others are strongly NP-hard by direct reduction from SAT. Finally, we give results on special graphs.