Parameterized Approximation Schemes using Graph Widths

TL;DR

This paper introduces a randomized rounding technique that provides approximation schemes for problems parameterized by graph widths like treewidth and clique-width, overcoming previous intractability and inapproximability barriers.

Contribution

It presents a novel, generic randomized rounding method that yields approximation schemes for problems parameterized by graph widths, bridging approximation algorithms and parameterized complexity.

Findings

Developed a versatile randomized rounding technique.

Achieved approximation schemes for problems hard to solve exactly.

Circumvented known intractability and inapproximability bounds.

Abstract

Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability of a number of problems which are known to be hard to solve exactly when parameterized by treewidth or clique-width. Our main contribution is to present a natural randomized rounding technique that extends well-known ideas and can be used for both of these widths. Applying this very generic technique we obtain approximation schemes for a number of problems, evading both polynomial-time inapproximability and parameterized intractability bounds.