This paper presents and solves in polynomial time the dynamic matching problem, an integer programming problem which involves matchings in a time-expanded infinite network. The initial model is a finite directed graph G = (V, E) in which each edge has an associated real-valued weight and an integral distance. We wish to "match" vertices over an infinite horizon, and we permit vertex i in period...

In this short note, we show that the Hamilton Cycle polynomial, ∑ n-cycles σ ∏n i=1 xi,σ(i) is not a monotone sub-exponential-size projection of the permanent; this both rules out a natural attempt at a monotone lower bound on the Boolean permanent, and shows that the permanent is not complete for non-negative polynomials in VNPR under monotone p-projections. We also show that the cut polynomia...

In this paper we show the rst polynomial-time algorithm for the problem of minimizing submodular functions on the product of diamonds of nite size. This submodular function minimization problem is reduced to the membership problem for an associated polyhedron, which is equivalent to the optimization problem over the polyhedron, based on the ellipsoid method. The latter optimization problem is a...

As a generalisation of the stable matching problem Bäıou and Balinski [3] defined the stable allocation problem for bipartite graphs, where both the edges and the vertices may have capacities. They constructed a so-called inductive algorithm, that always finds a stable allocation in strongly polynomial time. Here, we generalise their algorithm for non-bipartite graphs with integral capacities. ...

The forcing polynomial and anti-forcing are two important enumerative polynomials associated with all perfect matchings of a graph. In graph large order, the exhaustive enumeration which is used to compute number given matching too time-consuming number. this paper, we come up an efficient method — integer linear programming, matching. As applications, obtain di-forcing C60 , C70 C72 as consequ...

We describe a common generalization of the weighted matching problem and the weighted matroid intersection problem. In this context we establish common generalizations of the main results on those two problems|polynomial-time solvability, min-max theorems, and totally dual integral polyhedral descriptions. New applications of these results include a strongly polynomial separation algorithm for ...

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment-matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study the existence of such rules using algebraic techniques. These rules aim to improve the tractab...

A perfect matching in an undirected graph G = (V,E) is a set of vertex disjoint edges from E that include all vertices in V . The perfect matching problem is to decide if G has such a matching. Recently Rothvoß proved the striking result that the Edmonds’ matching polytope has exponential extension complexity. Here we describe a perfect matching polytope that is different from Edmonds’ polytope...

We introduce a class of counting problems that arise naturally in equational matching and study their computational complexity. If E is an equational theory, then #E-Matching is the problem of counting the number of complete minimal E-matchers of two given terms. #E-Matching is a well-deened algorithmic problem for every nitary equational theory. Moreover, it captures more accurately the comput...

An induced matching M of a graph G is a set of pairwise non-adjacent edges such that their end-vertices induce a 1-regular subgraph. An induced matching M is maximal if no other induced matching contains M . The MINIMUM MAXIMAL INDUCED MATCHING problem asks for a minimum maximal induced matching in a given graph. The problem is known to be NP-complete. Here we show that, if P 6= NP, for any ε >...