A new algorithm for Many to Many Matching with Demands and Capacities

TL;DR

This paper introduces an efficient algorithm for many-to-many point matching with demands and capacities, optimizing matchings between two point sets under specified constraints.

Contribution

It presents a novel O(n^4) time and O(n) space algorithm for the complex matching problem with demands and capacities.

Findings

Algorithm runs in O(n^4) time

Uses O(n) space

Effective for large-scale matching problems

Abstract

Let A={a_1,a_2,...,a_s} and {b_1,b_2,...,b_t} with s+r=n, the many to many point matching with demands and capacities matches each point a_i in A to at least alpha_i and at most alpha_i points in B, and each point b_j in B to at least beta_j and at most beta_j points in A for all 1 <= i <= s and 1 <= j <= t. In this paper, we present an O(n^4) time and O(n) space algorithm for this problem.