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2010

Polynomial-time dualization of r-exact hypergraphs with applications in geometry

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Polynomial-time dualization of r-exact hypergraphs with applications in geometry
Let H 2V be a hypergraph on vertex set V . For a positive integer r, we call H r-exact, if any minimal transversal of H intersects any hyperedge of H in at most r vertices. This class includes several interesting examples from geometry, e.g., circular-arc hypergraphs (r = 2), hypergraphs defined by sets of axis-parallel lines stabbing a given set of -fat objects (r = 4), and hypergraphs defined by sets of points contained in translates of a given cone in the plane (r = 2). For constant r, we give a polynomial-time algorithm for the duality testing problem of a pair of r-exact hypergraphs. This result implies that minimal hitting sets for the above geometric hypergraphs can be generated in output polynomial time.
Khaled M. Elbassioni, Imran Rauf
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2010
Where DM
Authors Khaled M. Elbassioni, Imran Rauf
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