In an instance of the house allocation problem, two sets A and B are given. The set A is referred to as applicants and the set B is referred to as houses. We denote by m and n the size of A and B respectively. In the house allocation problem, we assume that every applicant a ∈ A has a preference list over the set of houses B. We call an injective mapping τ from A to B a matching. A blocking coa...

A conjecture by Aharoni and Berger states that every family of n matchings of size n + 1 in a bipartite multigraph contains a rainbow matching of size n. In this paper we prove that matching sizes of ( 3 2 + o(1) ) n suffice to guarantee such a rainbow matching, which is asymptotically the same bound as the best-known one in the case where we only aim to find a rainbow matching of size n − 1. T...

Given a collection {Z1, Z2, . . . , Zm} of n-sided polygons in the plane and a query polygon W we give algorithms to find all Zl such that W = f(Zl) with f an unknown similarity transformation in time independent of the size of the collection. If f is a known affine transformation, we show how to find all Zl such that W = f(Zl) in O(n+ log(m)) time. For a pair W,W ′ of polygons we can find all ...

This paper presents a grid-based scan-to-map matching technique for accurate 2D map building. At every acquisition of a new scan, the proposed technique matches the new scan to the previous scan similarly to the conventional techniques, but further corrects the error by matching the new scan to the globally defined map. In order to achieve best scan-to-map matching at each acquisition, the map ...

Matching preclusion is a measure of robustness in the event of edge failure in interconnection networks. The matching preclusion number of a graph G is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching or an almost perfect matching, and the conditional matching preclusion number of G is the minimum number of edges whose deletion leaves the resultin...

Given a permutation P of f1; : : : ; kg and T of f1; : : : ; ng, the pattern matching problem for permutations is to determine whether there is a length k subsequence of T whose elements are ordered in the same way as the elements of P . We present an O(kn 4 ) time and O(kn 3 ) space algorithm for nding a match of P into T or determining that no match exists, given that P is separable, i.e. con...

Grinblat (2002) asks the following question in the context of algebras of sets: What is the smallest number v = v(n) such that, if A1, . . . , An are n equivalence relations on a common finite ground set X, such that for each i there are at least v elements of X that belong to Ai-equivalence classes of size larger than 1, then X has a rainbow matching—a set of 2n distinct elements a1, b1, . . ....

The energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G. We define the matching energy (ME) of the graph G as the sum of the absolute values of the zeros of the matching polynomial of G, and determine its basic properties. It is pointed out that the chemical applications of ME go back to the 1970s.

The random assignment (or bipartite matching) problem asks about An = minπ ∑ n i=1 c(i, π(i)), where (c(i, j)) is a n × n matrix with i.i.d. entries, say with exponential(1) distribution, and the minimum is over permutations π. Mézard and Parisi (1987) used the replica method from statistical physics to argue non-rigorously that EAn → ζ(2) = π /6. Aldous (1992) identified the limit in terms of ...

In this paper we answer a question posed by Sertel and Özkal-Sanver (2002) on the manipulability of optimal matching rules in matching problems with endowments. We characterize the classes of consumption rules under which optimal matching rules can be manipulated via predonation of endowment.