Abstract
In the online hypergraph matching problem, hyperedges of size k over a common ground set arrive online in adversarial order. The goal is to obtain a maximum matching (disjoint set of hyperedges). A naïve greedy algorithm for this problem achieves a competitive ratio of 1k. We show that no (randomized) online algorithm has competitive ratio better than 2+o(1)k. If edges are allowed to be assigned fractionally, we give a deterministic online algorithm with competitive ratio 1−o(1)ln(k) and show that no online algorithm can have competitive ratio strictly better than 1+o(1)ln(k). Lastly, we give a 1−o(1)ln(k) competitive algorithm for the fractional edge-weighted version of the problem under a free disposal assumption.
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