Speeding up deferred acceptance

TL;DR

This paper introduces an accelerated version of the deferred acceptance algorithm that reduces the number of rounds and proposals needed to find a stable matching, improving efficiency without affecting the outcome.

Contribution

The paper proposes a novel accelerated deferred acceptance algorithm that eliminates proposals guaranteed to be rejected, enhancing computational efficiency while maintaining the same stable matching.

Findings

Fewer rounds and proposals needed in the accelerated algorithm

Same stable matching as traditional DA achieved more efficiently

Efficiency gains can be strictly better in practice

Abstract

A run of the deferred acceptance (DA) algorithm may contain proposals that are sure to be rejected. We introduce the accelerated deferred acceptance algorithm that proceeds in a similar manner to DA but with sure-to-be rejected proposals ruled out. Accelerated deferred acceptance outputs the same stable matching as DA but does so more efficiently: it terminates in weakly fewer rounds, requires weakly fewer proposals, and final pairs match no later. Computational experiments show that these efficiency savings can be strict.