相关论文: Random multi-index matching problems

The multi-index matching is an NP-hard combinatorial optimization problem; for two indices it reduces to the well understood bipartite matching problem that belongs to the polynomial complexity class. We use the cavity method to solve the…

We study the random-link matching problem on random regular graphs, alongside with two relaxed versions of the problem, namely the fractional matching and the so-called "loopy" fractional matching. We estimated the asymptotic average…

Using the replica approach and the cavity method, we study the fluctuations of the optimal cost in the random-link matching problem. By means of replica arguments, we derive the exact expression of its variance. Moreover, we study the large…

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the…

Dirichlet process (DP) mixture models provide a flexible Bayesian framework for density estimation. Unfortunately, their flexibility comes at a cost: inference in DP mixture models is computationally expensive, even when conjugate…

We study the asymptotic behaviour of the expected cost of the random matching problem on a $2$-dimensional compact manifold, improving in several aspects the results of L. Ambrosio, F. Stra and D. Trevisan (A PDE approach to a 2-dimensional…

We consider a class of random matching problems where the distance between two points has a probability law which, for a small distance l, goes like l^r. In the framework of the cavity method, in the limit of an infinite number of points,…

We study the statistical mechanics of multi-index matching problems where the quenched disorder is a geometric site disorder rather than a link disorder. A recently developed functional formalism is exploited which yields exact results in…

The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree \mth{c} is larger than \mth{2.7183}, groups of max-matching patterns which differ greatly from…

Mixed Integer Programming (MIP) has been extensively applied in areas requiring mathematical solvers to address complex instances within tight time constraints. However, as the problem scale increases, the complexity of model formulation…

In this paper, we propose an algorithm referred to as multipath matching pursuit that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to…

Due to diverse nature of data acquisition and modern applications, many contemporary problems involve high dimensional datum $\x \in \R^\d$ whose entries often lie in a union of subspaces and the goal is to find out which entries of $\x$…

We analyse the asymptotic behaviour of random instances of the Maximum Set Packing (MSP) optimization problem, also known as Maximum Matching or Maximum Strong Independent Set on Hypergraphs. We give an analytical prediction of the MSPs…

Composite systems, where couplings are of two types, a combination of strong dilute and weak dense couplings of Ising spins, are examined through the replica method. The dilute and dense parts are considered to have independent canonical…

For data assumed to come from a finite mixture with an unknown number of components, it has become common to use Dirichlet process mixtures (DPMs) not only for density estimation, but also for inferences about the number of components. The…

Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that…

Visual framing analysis is a key method in social sciences for determining common themes and concepts in a given discourse. To reduce manual effort, image clustering can significantly speed up the annotation process. In this work, we phrase…

We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating…

In the context of disordered systems with quenched Hamiltonians I address the problem of characterizing rare samples where the thermal average of a specific observable has a value different from the typical one. These rare samples can be…

In this paper we rigorously prove the validity of the cavity method for the problem of counting the number of matchings in graphs with large girth. Cavity method is an important heuristic developed by statistical physicists that has lead to…