Finding minimally weighted subgraphs
WG '90 Proceedings of the 16th international workshop on Graph-theoretic concepts in computer science
Fast construction of irreducible polynomials over finite fields
Journal of Symbolic Computation
Handbook of combinatorics (vol. 1)
Handbook of combinatorics (vol. 1)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Parameterized coloring problems on chordal graphs
Theoretical Computer Science - Parameterized and exact computation
Parameterized Complexity
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Matroid theory gives us powerful techniques for understanding combinatorial optimization problems and for designing polynomial-time algorithms. However, several natural matroid problems, such as 3-matroid intersection, are NP-hard. Here we investigate these problems from the parameterized complexity point of view: instead of the trivial O(nk) time brute force algorithm for finding a k-element solution, we try to give algorithms with uniformly polynomial (i.e., f(k)nO(1)) running time. The main result is that if the ground set of a represented matroid is partitioned into blocks of size ℓ, then we can determine in f(k,ℓ)nO(1) randomized time whether there is an independent set that is the union of k blocks. As consequence, algorithms with similar running time are obtained for other problems such as finding a k-set in the intersection of ℓ matroids, or finding k terminals in a network such that each of them can be connected simultaneously to the source by ℓ disjoint paths.