Let G = (V,E) be a finite undirected graph without loops and multiple edges. A subset M ⊆ E of edges is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of M . In particular, this means that M is an induced matching, and every edge not in M shares exactly one vertex with an edge in M . Clearly, not every graph has a d.i.m. The Dominating Induced ...

Finding a maximum cardinality matching in a graph is a problem appearing in numerous settings. The problem asks for a set of edges of maximum cardinality, such that no two edges of this set have an endpoint in common. The variety of applications of this problem, along with the fact that several logic predicates can be modelled after it, motivates the study of a related global constraint in the ...

This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting Research supported by ESF. Research supported by the Austrian National Research Network S11403-N23 (RiSE) ...

In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching in the remaining graph is minimized. In this work we introduce the matching interdiction problem and show that it is strongly NP-complete even when the input ...

Multi-protocol attacks due to protocol interaction has been a notorious problem for security. Gutman-Thayer proved that they can be prevented by ensuring that encrypted messages are distinguishable across protocols, under a free algebra [1]. In this paper, we prove that a similar suggestion prevents these attacks under commonly used operators such as Exclusive-OR, that induce equational theorie...

Assignment problems are well-known problems in practice. We mention house markets, job markets, and production planning. The games of interest in this paper, the neighbor games, arise from a special class of assignment problems. We focus on the nucleolus [D. Schmeidler, SIAM J. Appl. Math. 17 (1969) 1163–1170], one of the most prominent core solutions. A core solution is interesting with respec...

In this paper, we show that the truly two-dimensional elastic image matching problem can be solved analytically using dynamic programming (DP) in polynomial time if the problem is formulated as a maximum a posteriori problem using Gaussian distributions for the likelihood and prior. After giving the derivation of the analytical DP matching algorithm, we evaluate its performance on handwritten c...

This paper presents a polynomial time algorithm (pruned correspondence search, PCS) for solving a wide class of geometric maximal matching problems, including the problem of recognizing 3D objects from a single 2D image. The PCS algorithm is connected with the geometry of the underlying recognition problem only through calls to a verification algorithm.

We present estimates on the small singular values of a class of matrices with independent Gaussian entries and inhomogeneous variance profile, satisfying a broad-connectedness condition. Using these estimates and concentration of measure for the spectrum of Gaussian matrices with independent entries, we prove that for a large class of graphs satisfying an appropriate expansion property, the Bar...

It is a longstanding open problem whether there exists a polynomial size description of the perfect matching polytope. We give a partial answer to this question by proving the following result. The polyhedron defined by the constraints of the perfect matching polytope which are active at a given perfect matching can be obtained as the projection of a compact polyhedron. Thus there exists a comp...