An efficient algorithm for the limited-capacity many-to-many point matching in one dimension

Fatemeh Rajabi-Alni, Behrouz Minaei-Bidgoli, Alireza Bagheri

Abstract: Matching elements from two sets (bipartite matching), a fundamental subject in computer science, is used in applications such as bipartite data matching (e.g. graph edit distance computation and semantic data matching) and allocating resources in a wireless network. Given two sets S and T, a limited-capacity many-to-many matching (LCMM) between S and T matches each element p in S (resp. T) to at least 1 and at most Cap(p) elements in T (resp. S), where the function \(Cap:S\cup T\rightarrow \mathbb {Z}>0\) denotes the capacity of p. In this paper, we present the first linear time algorithm for finding a minimum-cost one-dimensional LCMM (OLCMM) between S and T when S and T are points lying on a line; the cost of matching each point \(p\in S\) to \(q\in T\) equals the Euclidean distance between p, q. Our dynamic programming algorithm improves the previous best-known quadratic time algorithm, and moreover, can be used with online arriving input points (which are not known in advance and arrive sequentially one by one).

External IDs:dblp:journals/tjs/RajabiAlniMB25