Beyond matroids: Secretary Problem and Prophet Inequality with general constraints

Aviad Rubinstein

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arXiv · 1604.00357

Beyond matroids: Secretary Problem and Prophet Inequality with general constraints

Aviad Rubinstein

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Abstract

We study generalizations of the "Prophet Inequality" and "Secretary Problem", where the algorithm is restricted to an arbitrary downward-closed set system. For {0,1}-values, we give O(log n)-competitive algorithms for both problems. This is close to the \Omega(log n / loglog n) lower bound due to Babaioff, Immorlica, and Kleinberg. For general values, our results translate to O(log n log r)-competitive algorithms, where r is the cardinality of the largest feasible set. This resolves (up to the O(log r loglog n) factors) an open question posed to us by Bobby Kleinberg.

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Aviad Rubinstein. 2016-04-01. Beyond matroids: Secretary Problem and Prophet Inequality with general constraints. https://arxiv.org/abs/1604.00357

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