Partitioning algorithms for the Euclidean matching and for the semimatching problem in the plane are introduced and analysed. The algorithms are analogues of Karp’s well-known dissection algorithm for the traveling salesman problem. The algorithms are proved to run in time n log n and to approximate the optimal matching in the probabilistic sense. The analysis is based on the techniques develop...

For a graph consider the pairs of disjoint matchings which union contains as many edges as possible, and define a parameter α which eqauls the cardinality of the largest matching in those pairs. Also, define β to be the cardinality of a maximum matching of the graph. We give a constructive characterization of trees which satisfy the α = β equality. The proof of our main theorem is based on a ne...

1 Petersen’s Theorem Recall that a graph is cubic if every vertex has degree exactly 3, and bridgeless if it cannot be disconnected by deleting any one edge (i.e., 2-edge-connected). Theorem 1 (Petersen) Any bridgeless cubic graph has a perfect matching. Proof: We will show that for any V ⊆ U , we have o(G−U) ≤ |U | (here o(G) is the number of odd components of the graph G). The theorem will th...

Pattern matching, the problem of finding sub sequences within a long sequence is essential for many applications such as information retrieval, disease analysis, structural and functional analysis, logic programming, theorem-proving, term rewriting and DNA-computing. In computational biology the essential components for DNA applications is the exact string matching algorithms. Many databases li...

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually ratio...

In K(n, n) with edges colored either red or blue, we show that the problem of finding a solution matching, a perfect matching consisting of exactly r red edges, and (n− r) blue edges for specified 0 ≤ r ≤ n, is a nontrivial integer program. We present an alternative, logically simpler proof of a theorem in [3] which establishes necessary and sufficient conditions for the existance of a solution...

This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has been popular in the economics and genetics literatures. We construct a joint agent-probability space, and randomized mutation, partial matching and match-induced type-changing functions that satisfy appropriate independence conditions. The proofs are achi...

We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a “double stable” matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets the associated stable c...

We present a tool which allows implicit VDM speciications to be used as search keys for the retrieval of software components. A preprocessing phase utilizes signature matching to lter promising candidates out of a component library. The actual speciication matching phase builds proof obligations from the speciications of key and candidates and feeds them into a theorem prover. Validated obligat...

Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of indirect dominance, we investigate von Neumann-Morgenstern farsightedly stable sets. We show that a singleton is von Neumann-Morgenster...