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

Let A = {a1, a2, . . . , as} and {b1, b2, . . . , bt} with s+r = n, the many to many point matching with demands and capacities matches each point ai ∈ A to at least αi and at most α ′ i points in B, and each point bj ∈ B to at least βj and at most β ′j points in A for all 1 ≤ i ≤ s and 1 ≤ j ≤ t. In this paper, we present an O(n) time and O(n) space algorithm for this problem.