algo-hr-matching
Gale-Shapley Stable Matching
Overview
Gale-Shapley (deferred acceptance) finds a stable matching between two equally-sized sets where no unmatched pair prefers each other over their current match. Runs in O(n²) worst case. Proposer-optimal: the proposing side gets their best stable partner.
When to Use
Trigger conditions:
- Matching candidates to job positions based on mutual preferences
- Assigning students to schools or residents to hospitals
- Any two-sided matching where stability (no blocking pairs) is required
When NOT to use:
- For one-sided assignment (use Hungarian algorithm)
- When preferences are based on scores, not rankings (use optimization)
Algorithm
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