NP-hard graph problems and boundary classes of graphs

NP-hard graph problems and boundary classes of graphs

Any graph problem, which is NP-hard in general graphs, becomes polynomial-time solvable when restricted to graphs in special classes. When does a difficult problem become easy? To answer this question we study the notion of boundary classes. In the present paper we define this notion in its most general form, describe several approaches to identify boundary classes and apply them to various gra...

How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time

How to solve NP-hard graph problems on lique-width bounded graphs in polynomial time

Linear Problem Kernels for NP-Hard Problems on Planar Graphs

We develop a generic framework for deriving linear-size problem kernels for NP-hard problems on planar graphs. We demonstrate the usefulness of our framework in several concrete case studies, giving new kernelization results for Connected Vertex Cover, Minimum Edge Dominating Set,Maximum Triangle Packing, and Efficient Dominating Set on planar graphs. On the route to these results, we present e...

Lecture 29: Np-hard Problems [fa'12] 29 Np-hard Problems 29.1 'efficient' Problems

A generally-accepted minimum requirement for an algorithm to be considered ‘efficient’ is that its running time is polynomial: O(nc) for some constant c, where n is the size of the input.1 Researchers recognized early on that not all problems can be solved this quickly, but we had a hard time figuring out exactly which ones could and which ones couldn’t. there are several so-called NP-hard prob...