43,509 research outputs found
Integrality Gap of the Hypergraphic Relaxation of Steiner Trees: a short proof of a 1.55 upper bound
Recently Byrka, Grandoni, Rothvoss and Sanita (at STOC 2010) gave a
1.39-approximation for the Steiner tree problem, using a hypergraph-based
linear programming relaxation. They also upper-bounded its integrality gap by
1.55. We describe a shorter proof of the same integrality gap bound, by
applying some of their techniques to a randomized loss-contracting algorithm
Parameterized Approximation Schemes using Graph Widths
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
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