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ICALP

2009

Springer

2009

Springer

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...

Related Content

Added |
03 Dec 2009 |

Updated |
03 Dec 2009 |

Type |
Conference |

Year |
2009 |

Where |
ICALP |

Authors |
Ioannis Koutis, Ryan Williams |

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