Kernelization Lower Bounds for Finding Constant Size Subgraphs
share
Kernelization is an important tool in parameterized algorithmics. The goal is to reduce the input instance of a parameterized problem in polynomial time to an equivalent instance of the same problem such that the size of the reduced instance only depends on the parameter and not on the size of the original instance. In this paper, we provide a first conceptual study on limits of kernelization for several polynomial-time solvable problems. For instance, we consider the problem of finding a triangle with negative sum of edge weights parameterized by the maximum degree of the input graph. We prove that a linear-time computable strict kernel of truly subcubic size for this problem violates the popular APSP-conjecture.
READ FULL TEXT