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ICALP
2009
Springer

Limits and Applications of Group Algebras for Parameterized Problems

11 years 4 months ago
Limits and Applications of Group Algebras for Parameterized Problems
The algebraic framework introduced in [Koutis, Proc. of the 35th ICALP 2008] reduces several combinatorial problems in parameterized complexity to the problem of detecting multilinear degree-k monomials in polynomials presented as circuits. The best known (randomized) algorithm for this problem requires only O (2k ) time and oracle access to an arithmetic circuit, i.e. the ability to evaluate the circuit on elements from a suitable group algebra. This algorithm has been used to obtain the best known algorithms for several parameterized problems. In this paper we use communication complexity to show that the O (2k ) algorithm is essentially optimal within this evaluation oracle framework. On the positive side, we give new applications of the method: finding a copy of a given tree on k nodes, a spanning tree with at least k leaves, a minimum set of nodes that dominate at least t nodes, and an m-dimensional k-matching. In each case we achieve a faster algorithm than what was known. We al...
Ioannis Koutis, Ryan Williams
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2009
Where ICALP
Authors Ioannis Koutis, Ryan Williams
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