Algorithms for Secretary Problems on Graphs and Hypergraphs

12 years 9 months ago
Algorithms for Secretary Problems on Graphs and Hypergraphs
We examine several online matching problems, with applications to Internet advertising reservation systems. Consider an edge-weighted bipartite graph G, with partite sets L, R. We develop an 8-competitive algorithm for the following secretary problem: Initially given R, and the size of L, the algorithm receives the vertices of L sequentially, in a random order. When a vertex l L is seen, all edges incident to l are revealed, together with their weights. The algorithm must immediately either match l to an available vertex of R, or decide that l will remain unmatched. In [4], the authors show a 16-competitive algorithm for the transversal matroid secretary problem, which is the special case with weights on vertices, not edges. (Equivalently, one may assume that for each l L, the weights on all edges incident to l are identical.) We use a similar algorithm, but simplify and improve the analysis to obtain a better competitive ratio for the more general problem. Perhaps of more interest ...
Martin Pál, Nitish Korula
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2009
Authors Martin Pál, Nitish Korula
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