Many to Many Matching with Demands and Capacities

TL;DR

This paper introduces a polynomial time algorithm for solving the many-to-many point matching problem with demands and capacities, providing an upper bound for the problem's solution.

Contribution

The paper presents a novel polynomial time algorithm and an upper bound for the many-to-many matching problem with demands and capacities.

Findings

Algorithm operates in polynomial time

Provides an upper bound for the matching problem

Addresses constraints of demands and capacities

Abstract

Let A and B be two finite sets of points with total cardinality n, the many to many point matching with demands and capacities matches each point ai in A to at least alpha'i and at most alphai points in B, and each point bj in B to at least betaj and at most beta'j points in A for all 1 <= i <= s and 1 <= j <= t. In this paper, we present an upper bound for this problem using our new polynomial time algorithm.