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> JAN 29: Theory: Combinatorics CS Seminar
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JAN 29: Theory: Combinatorics CS Seminar
Event date: Friday, January 29, 2010, at 2:00 PM
Location: Sandford Flemming Bldg. Rm SF3207
Speaker: Christophe Paul,
LIRMM, Universite de Montpellier
Topic: A linear vertex kernel for the feedback arc set problem in tournaments and some applications of modular decomposition in fixed parameter algorithms.
Abstract:
The existence of a fixed parameterized (FPT) algorithm for a parameterized problem is known to be equivalent to the existence of a kernelization algorithm: a polytime algorithm that reduces the parameterized instance to an equivalent instance whose size is bounded by a function of the parameter only. The question for a FPT problem is whether or not it admits a polynomial (in the parameter) size kernel. After a brief introduction to kernelization techniques, the talk contains two parts:
1)
Parameterized Feedback Arc Set in Tournaments.
A tournament T = (V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs whose removal results in an acyclic digraph. The Feedback Arc Set problem restricted to tournaments is known as the k-Feedback Arc Set in Tournaments (k-FAST) problem. In this talk, we present a linear vertex kernel for k-FAST. That is, we give a polynomial time algorithm which given an input instance T to k-FAST obtains an equivalent instance T' on O(k) vertices. In fact, given any fixed \epsilon > 0, the kernelized instance has at most (2 + \epsilon)k vertices. Our result improves the previous known bound of O(k^2) on the kernel size for k-FAST. Our kernelization algorithm solves the problem on a subclass of tournaments in polynomial time and uses a known polynomial time approximation scheme for k-FAST.
2)
Modular decomposition and polynomial size kernels.
One of the reduction rules of our kernelization algorithm deals with the existence of a large (with respect to k) transitive module in a non reduced instance. In the last few years, a few kernelization results have been obtained for parameterized graph modification problems such as cluster editing. We give a brief overview of these known polynomial kernels.
For Additional Information, Contact: Derek Corneil