Consider a bipartite graph; let’s suppose we draw the origin nodes and the destination nodes arranged in two columns, and the edges as straight-line segments. A noncrossing matching is a subset of edges such that no two of them intersect. Several algorithms for the problem of finding the noncrossing matching of maximum cardinality are proposed. Moreover an extension to weighted graphs is considered.
Efficient labelling algorithms for the maximum noncrossing matching problem / F., Malucelli; T., Ottmann; Pretolani, Daniele. - In: DISCRETE APPLIED MATHEMATICS. - ISSN 0166-218X. - STAMPA. - 47 (2):(1993), pp. 175-179. [10.1016/0166-218X(93)90090-B]