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/log1 − 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.
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Czumaj, A., Lingas, A., Nilsson, J. (2003). Improved Approximation Algorithms for Optimization Problems in Graphs with Superlogarithmic Treewidth. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_56
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DOI: https://doi.org/10.1007/978-3-540-24587-2_56
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