We propose a new approach for the study of the quadratic stochastic Euclidean bipartite matching problem between two sets of N points each, N 1. The points are supposed independently randomly generated on a domain Ω ⊂ Rd with a given distribution ρ(x) on Ω. In particular, we derive a general expression for the correlation function and for the average optimal cost of the optimal matching. A prev...

We study a class of functional which can be used for matching objects which can be represented as mappings from a fixed interval, I, to some “feature space.” This class of functionals corresponds to “elastic matching” in which a symmetry condition and a “focus invariance” are imposed. We provide sufficient conditions under which an optimal matching can be found between two such mappings, the op...

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...

To facilitate the damping matching of dampers for vehicle passive suspensions, this paper proposes an analytical matching method of the optimal piecewise linear damping characteristics curve. Based on the vehicle vibration model, taking the suspension dynamic deflection as the constraint, by the vibration acceleration and the wheel dynamic load, an objective function about the relative damping ...

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.

The damping ratio of chassis suspension is a key parameter for damping matching of in-wheel motor vehicles (IWMVs). Because the motor is attached to the driving wheel, the initial design method of the damping ratio for traditional cars is not entirely suitable for IWMVs. This paper proposes an innovative initial design method of the damping ratio for IWMVs. Firstly, a traveling vibration model ...