In this paper we study the classic problem of computing a maximum cardinality matching in general graphs $G = (V, E)$. This problem has been studied extensively more than four decades. The best known algorithm for this problem till date runs in $O(m \sqrt{n})$ time due to Micali and Vazirani ... more >>>

We establish almost tight upper and lower approximation bounds for the Vertex Cover problem on dense k-partite hypergraphs.

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We study the lift-and-project procedures of Lovasz-Schrijver and Sherali-Adams applied to the standard linear programming relaxation of the traveling salesperson problem with triangle inequality. For the asymmetric TSP tour problem, Charikar, Goemans, and Karloff (FOCS 2004) proved that the integrality gap of the standard relaxation is at least 2. We ... more >>>