PT Unknown AU El Ouali, M TI Randomized Approximation for the Matching and Vertex Cover Problem in Hypergraphs: Complexity and Algorithms PY 2013 PU Christian-Albrechts-Universität zu Kiel WP https://macau.uni-kiel.de/receive/diss_mods_00013153 LA en DE Approximation Algorithms; Hypergraphs; Complexity; Inapproximability; Optimization Problems; ComplexitApproximationsalgorithmen; Hypergraphen; Komplexität; Nicht-Approximierbarkeit; Optimierungsprobleme AB This thesis studies the design and mathematical analysis of randomized approximation algorithms for the hitting set and b-matching problems in hypergraphs. We present a randomized algorithm for the hitting set problem based on linear programming. The analysis of the randomized algorithm rests upon the probabilistic method, more precisely on some concentration inequalities for the sum of independent random variables plus some martingale based inequalities, as the bounded difference inequality, which is a derived from Azuma inequality. In combination with combinatorial arguments we achieve some new results for different instance classes that improve upon the known approximation results for the problem (Krevilevich (1997), Halperin (2001)). We analyze the complexity of the b-matching problem in hypergraphs and obtain two new results. We give a polynomial time reduction from an instance of a suitable problem to an instance of the b-matching problem and prove a non-approximability ratio for the problem in l-uniform hypergraphs. This generalizes the result of Safra et al. (2006) from b=1 to b in O(l/log(l)). Safra et al. showed that the 1-matching problem in l-uniform hypergraphs can not be approximated in polynomial time within a ratio O(l/log(l)), unless P = NP. Moreover, we show that the b-matching problem on l-uniform hypergraphs with bounded vertex degree has no polynomial time approximation scheme PTAS, unless P=NP. PI Kiel ER