Randomized Algorithm for MPMD on Two Sources

A 3-competitive deterministic algorithm for the problem of min-cost perfect matching with delays on two sources (2-MPMD) was proposed years ago. However, whether randomness leads to a more competitive algorithm remains open. 2-MPMD is similar to the famous ski rental problem. Indeed, for both problems, we must choose between continuing to pay a repeating cost or a one-time fee. There is a memoryless randomized algorithm for ski rental that is more competitive than its best deterministic algorithm. But, surprisingly, memoryless randomized algorithms for 2-MPMD cannot do better than 3-competitive. In this paper, we devise a 2-competitive randomized algorithm for 2-MPMD. Moreover, we prove that 2 is also the lower bound.