Prophet Matching Meets Probing with Commitment
Allan Borodin, Calum MacRury, Akash Rakheja

TL;DR
This paper introduces new algorithms and LP relaxations for online stochastic bipartite matching with commitment and probing constraints, achieving improved competitive ratios in various stochastic settings.
Contribution
It develops a novel LP relaxation and provides tight competitive ratios for different stochastic models, advancing the understanding of probing with commitment in online matching.
Findings
Achieves a 1/2 competitive ratio in adversarial type graph setting.
Achieves a 1-1/e competitive ratio in random order setting.
Improves previous best ratio of 0.46 in the known i.i.d. setting.
Abstract
We consider the online stochastic matching problem for bipartite graphs where edges adjacent to an online node must be probed to determine if they exist, based on known edge probabilities. Our algorithms respect commitment, in that if a probed edge exists, it must be used in the matching. We study this matching problem subject to a downward-closed constraint on each online node's allowable edge probes. Our setting generalizes the commonly studied patience (or time-out) constraint which limits the number of probes that can be made to an online node's adjacent edges. We introduce a new LP that we prove is a relaxation of an optimal offline probing algorithm (the adaptive benchmark) and which overcomes the limitations of previous LP relaxations. (1) A tight ratio when the stochastic graph is generated from a known stochastic type graph where the online node is…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
