The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete
SIAM Journal on Algebraic and Discrete Methods
Algorithmics for Hard Problems
Algorithmics for Hard Problems
Improved Approximation Algorithms for Resource Allocation
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation Algorithms for the Unsplittable Flow Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Call control with k rejections
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Parameterized Complexity
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We study an NP-hard (and MaxSNP-hard) problem in trees-Multicommodity Demand Flow-dealing with demand flows between pairs of nodes and trying to maximize the value of the routed flows. This problem has been intensively studied for trees as well as for general graphs mainly from the viewpoint of polynomial-time approximation algorithms. By way of contrast, we provide an exact dynamic programming algorithm for this problem that works well whenever some natural problem parameter is small, a reasonable assumption in several applications. More specifically, we prove fixed-parameter tractability with respect to the maximum number of the input flows at any tree node.