Constrained Matchings in Bipartite Graphs

14 Pages Posted: 2 Dec 2012

See all articles by Andrea Borghesan

Andrea Borghesan

Ca Foscari University of Venice

Daniela Favaretto

Ca Foscari University of Venice - Department of Management

Francesco Mason

Ca Foscari University of Venice - Department of Management

Date Written: November 30, 2012

Abstract

We consider some particular cases of the general problem which consists of stating if a shift vector of m elements corresponds to a permutation of the same number of objects. Shifts are defined as the steps each element in a given permutation must perform in order to reach its natural position, i.e., to its position in the fundamental permutation, (1, 2, ..., m). The problem, never studied at our knowledge, was suggested to us by a paper in which a certain number of vehicles must be moved from initial to nal positions in a grid graph in such a way that vehicles do not share the same vertex at the same time. The problem can also be stated in terms of a covering one, i.e. the vertex cover of a particular graph, with cycle using arcs of de ned lengths. Some properties of the shift vector, necessary in order to guarantee the existence of a corresponding permutation, and a general algorithm to find the permutations, if they exist, are given.

Keywords: Cycle covering, Permutations

JEL Classification: C61, C63

Suggested Citation

Borghesan, Andrea and Favaretto, Daniela and Mason, Francesco, Constrained Matchings in Bipartite Graphs (November 30, 2012). Department of Management, Università Ca' Foscari Venezia Working Paper No. 22/2012, Available at SSRN: https://ssrn.com/abstract=2183358

Andrea Borghesan

Ca Foscari University of Venice ( email )

Dorsoduro 3246
Venice, Veneto 30123
Italy

Daniela Favaretto

Ca Foscari University of Venice - Department of Management ( email )

San Giobbe, Cannaregio 873
Venice, 30121
Italy

Francesco Mason (Contact Author)

Ca Foscari University of Venice - Department of Management ( email )

San Giobbe, Cannaregio 873
Venice, 30121
Italy

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