# Anytime Heuristic for Weighted Matching Through Altruism-Inspired Behavior

## TL;DR

This paper introduces ALMA, a decentralized, altruism-inspired heuristic for the assignment problem that converges quickly and scales efficiently, outperforming centralized algorithms in large, realistic scenarios.

## Contribution

The paper proposes a novel altruism-inspired, decentralized heuristic for weighted matching with proven polynomial convergence bounds and demonstrated scalability and efficiency in practical tests.

## Key findings

- ALMA achieves high social welfare in diverse scenarios.
- ALMA converges orders of magnitude faster than optimal centralized algorithms.
- ALMA scales to hundreds of thousands of agents in urban vehicle coordination.

## Abstract

We present a novel anytime heuristic (ALMA), inspired by the human principle of altruism, for solving the assignment problem. ALMA is decentralized, completely uncoupled, and requires no communication between the participants. We prove an upper bound on the convergence speed that is polynomial in the desired number of resources and competing agents per resource; crucially, in the realistic case where the aforementioned quantities are bounded independently of the total number of agents/resources, the convergence time remains constant as the total problem size increases. We have evaluated ALMA under three test cases: (i) an anti-coordination scenario where agents with similar preferences compete over the same set of actions, (ii) a resource allocation scenario in an urban environment, under a constant-time constraint, and finally, (iii) an on-line matching scenario using real passenger-taxi data. In all of the cases, ALMA was able to reach high social welfare, while being orders of magnitude faster than the centralized, optimal algorithm. The latter allows our algorithm to scale to realistic scenarios with hundreds of thousands of agents, e.g., vehicle coordination in urban environments.