Matching with our Eyes Closed
Gagan Goel, Pushkar Tripathi

TL;DR
This paper introduces a new randomized greedy algorithm for the query-commit matching problem, achieving a 56% approximation ratio and establishing bounds on the best possible performance of such algorithms.
Contribution
It proposes a novel randomized greedy algorithm with a 0.56 approximation factor and provides upper bounds for the performance of all randomized and vertex-iterative algorithms.
Findings
New randomized greedy algorithm attains at least 0.56 approximation.
No randomized algorithm can surpass 0.7916 approximation.
Vertex-iterative algorithms cannot exceed 0.75 approximation.
Abstract
Motivated by an application in kidney exchange, we study the following query-commit problem: we are given the set of vertices of a non-bipartite graph G. The set of edges in this graph are not known ahead of time. We can query any pair of vertices to determine if they are adjacent. If the queried edge exists, we are committed to match the two endpoints. Our objective is to maximize the size of the matching. This restriction in the amount of information available to the algorithm constraints us to implement myopic, greedy-like algorithms. A simple deterministic greedy algorithm achieves a factor 1/2 which is tight for deterministic algorithms. An important open question in this direction is to give a randomized greedy algorithm that has a significantly better approximation factor. This question was first asked almost 20 years ago by Dyer and Frieze [9] where they showed that a natural…
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.
Taxonomy
TopicsOptimization and Search Problems · Complexity and Algorithms in Graphs · Cryptography and Data Security
