On the k-coloring of intervals
Discrete Applied Mathematics
Online computation and competitive analysis
Online computation and competitive analysis
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The edge-disjoint path problem is NP-complete for series-parallel graphs
Discrete Applied Mathematics - Special issue on selected papers from First Japanese-Hungarian Symposium for Discrete Mathematics and its Applications
The Maximum Edge-Disjoint Paths Problem in Bidirected Trees
SIAM Journal on Discrete Mathematics
Strongly Polynomial Algorithms for the Unsplittable Flow Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation Algorithms and Complexity Results for Path Problems in Trees of Rings
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Admission Control to Minimize Rejections
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Vertex Cover: Further Observations and Further Improvements
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
An efficient fixed-parameter algorithm for 3-hitting set
Journal of Discrete Algorithms
Parameterized Complexity
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Given a set of connection requests (calls) in a communication network, the call control problem is to accept a subset of the requests and route them along paths in the network such that no edge capacity is violated, with the goal of rejecting as few requests as possible. We investigate the complexity of parameterized versions of this problem, where the number of rejected requests is taken as the parameter. For the variant with pre-determined paths, the problem is fixed-parameter tractable in arbitrary graphs if the link capacities are bounded by a constant, but W[2]-hard if the link capacities are arbitrary. If the paths are not pre-determined, no FPT algorithm can exist even in series-parallel graphs unless P = NP. Our main results are newFPT algorithms for call control in tree networks with arbitrary edge capacities and in trees of rings with unit edge capacities in the case that the paths are not pre-determined.