Integer and combinatorial optimization
Integer and combinatorial optimization
An almost linear-time algorithm for graph realization
Mathematics of Operations Research
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Approximating k-Set Cover and Complementary Graph Coloring
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Practical Algorithms on Partial k-Trees with an Application to Domination-like Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Refined memorization for vertex cover
Information Processing Letters
Parameterized Complexity
Parameterized algorithms for weighted matching and packing problems
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A dynamic programming algorithm for tree-like weighted set packing problem
Information Sciences: an International Journal
Minimum membership set covering and the consecutive ones property
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Complexity and exact algorithms for multicut
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
The parameterized complexity of enumerating frequent itemsets
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Tree decompositions of graphs: Saving memory in dynamic programming
Discrete Optimization
Parameterized algorithms for weighted matching and packing problems
Discrete Optimization
Efficient derivation of numerical dependencies
Information Systems
The complexity of weighted counting for acyclic conjunctive queries
Journal of Computer and System Sciences
Computing cooperative solution concepts in coalitional skill games
Artificial Intelligence
Hi-index | 0.00 |
We introduce an NP-complete special case of the Weighted Set Cover problem and show its fixed-parameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given collection C of subsets of a base set S should be ''tree-like''. That is, the subsets in C can be organized in a tree T such that every subset one-to-one corresponds to a tree node and, for each element s of S, the nodes corresponding to the subsets containing s induce a subtree of T. This is equivalent to the problem of finding a minimum edge cover in an edge-weighted acyclic hypergraph. Our main result is an algorithm running in O(3^k@?mn) time where k denotes the maximum subset size, n:=|S|, and m:=|C|. The algorithm also implies a fixed-parameter tractability result for the NP-complete Multicut in Trees problem, complementing previous approximation results. Our results find applications in computational biology in phylogenomics and for saving memory in tree decomposition based graph algorithms.