Diminishable parameterized problems and strict polynomial kernelization

Diminishable Parameterized Problems and Strict Polynomial Kernelization

Kernelization—a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems—plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a lower bounds framework that allows to exclude polynomial-size kernels under the assumption of NP * coNP/poly. In this paper we consider a restricted yet natural...

5. Kernelization - COMP6741: Parameterized and Exact Computation

6. Kernelization - COMP6741: Parameterized and Exact Computation

Kernelization of packing problems

Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d ≥ 3 is the problem of nding a matching of size at least k in a given d-uniform hypergraph and has kernels with O(k) edges. Recently, Bodlaender et al. [ICALP 2008], Fortnow and Santhanam [STOC 2008], Dell...

Kernelization and Parameterized Algorithms for 3-Path Vertex Cover

A 3-path vertex cover in a graph is a vertex subset C such that every path of three vertices contains at least one vertex from C. The parameterized 3-path vertex cover problem asks whether a graph has a 3-path vertex cover of size at most k. In this paper, we give a kernel of 5k vertices and an O(1.7485)-time polynomial-space algorithm for this problem, both new results improve previous known b...