
TL;DR
This paper investigates online secretary problems with returns in combinatorial packing domains, proposing algorithms with competitive ratios for maximum value packing and analyzing the expected postponements in candidate decision-making.
Contribution
It introduces new algorithms for secretary problems with returns, achieving improved competitive ratios and analyzing postponement bounds in various packing and matroid settings.
Findings
Proposes a 0.5-competitive algorithm for candidates arriving twice.
Achieves at least 0.5721 competitive ratio for bipartite matching with returns.
Shows expected postponements can be reduced to O(r log(n/r)) in matroids.
Abstract
We study online secretary problems with returns in combinatorial packing domains with candidates that arrive sequentially over time in random order. The goal is to accept a feasible packing of candidates of maximum total value. In the first variant, each candidate arrives exactly twice. All arrivals occur in random order. We propose a simple 0.5-competitive algorithm that can be combined with arbitrary approximation algorithms for the packing domain, even when the total value of candidates is a subadditive function. For bipartite matching, we obtain an algorithm with competitive ratio at least for growing , and an algorithm with ratio at least for all . We extend all algorithms and ratios to arrivals per candidate. In the second variant, there is a pool of undecided candidates. In each round, a random candidate from the pool…
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