Approximately Counting Perfect And General Matchings in Bipartite and General Graphs

In this paper we extend the matching technique to a class of nonholonomic systems with symmetries. Assuming that the momentum equation defines an integrable distribution, we introduce a family of reduced systems. The method of controlled Lagrangians is then applied to these systems resulting in a smooth stabilizing controller.

In this paper, we propose an algorithm for enumerating all the perfect matchings included in a given bipartite graph G = (V,E). The algorithm is improved by the approach which we proposed at ISAAC98. Our algorithm takes O(log |V |) time per perfect matching while the current fastest algorithm takes O(|V |) time per perfect matching. Keyword: enumeration, enumerating algorithm, perfect matching.

The symmetry of the joint distribution of the numbers of crossings and nestings of length 2 has been observed in many combinatorial structures, including permutations, matchings, set partitions, linked partitions, and certain families of graphs. These results have been unified in the larger context of enumeration of northeast and southeast chains of length 2 in 01-fillings of moon polyominoes. ...

A matching in a graph is a collection of edges, no two of which share a

In this paper it is shovm that every maximum matching in a 3-connectccl graph, other than ](4, contains at least one contractible edge. In the case of a. perfect ma.tching, those graphs in \vhich there exists a perfect matching containing precisely one contractible edge arc characterized.

A fractional matching of a graph G is a function f from E(G) to the interval [0, 1] such that ∑ e∈Γ(v) f(e) ≤ 1 for each v ∈ V (G), where Γ(v) is the set of edges incident to v. The fractional matching number of G, written α′∗(G), is the maximum of

Let A and B be two sets of m resp. n weighted points in the plane, with m ≤ n. We present (1 + 6) and (2+6)-approximation algorithms for the minimum Euclidean Earth Mover’s Distance between A and B under translations and rigid motions respectively. In the general case where the sets have unequal total weights the algorithms run in O((nm/6) log(n/6)) time for translations and O((nm/6) log(n/6)) ...

We say that a graph G is k-Pfaffian if the generating function of its perfect matchings can be expressed as a linear combination of Pfaffians of k matrices corresponding to orientations of G. We prove that 3-Pfaffian graphs are 1-Pfaffian, 5-Pfaffian graphs are 4-Pfaffian and that a graph is 4-Pfaffian if and only if it can be drawn on the torus (possibly with crossings) so that every perfect m...