Improved Approximation Algorithms for Optimization Problems in Graphs with Superlogarithmic Treewidth

Abstract

In this paper we present two novel generic schemes for approximation algorithms for optimization $\mathcal{NP}$-hard graph problems constrained to partial k-trees. Our first scheme yields deterministic polynomial-time algorithms achieving typically an approximation factor of k/log^1 − ε n, where k = polylog (n). The second scheme yields randomized polynomial-time algorithms achieving an approximation factor of k / log n for k = ω(log n). Both our approximation methods lead to the best known approximation guarantees for some basic optimization problems. In particular, we obtain best known polynomial-time approximation guarantees for the classical maximum independent set problem in partial trees.