In 1979 Kazhdan and Lusztig defined, for every Coxeter group W , a family of polynomials, indexed by pairs of elements ofW , which have become known as the Kazhdan-Lusztig polynomials of W , and which have proven to be of importance in several areas of mathematics. In this paper we show that the combinatorial concept of a special matching plays a fundamental role in the computation of these pol...

A minimal blocker in a bipartite graph G is a minimal set of edges the removal of which leaves no perfect matching in G. We give a polynomial delay algorithm for finding all minimal blockers of a given bipartite graph. Equivalently, this gives a polynomial delay algorithm for listing the anti-vertices of the perfect matching polytope P (G) = {x ∈ R | Hx = e, x ≥ 0}, where H is the incidence mat...

In this paper a novel technique for rotation independent template matching via Quadtree Zernike decomposition is presented. Both the template and the target image are decomposed by using a complex polynomial basis. The template is analyzed in block-based manner by using a quad tree decomposition. This allows the system to better identify the object features. Searching for a complex pattern into...

A simple way to calculate the number of k-matchings, k ~< 5, in hexagonal systems is presented. Some relations between the coefficients of the characteristic polynomial of the adjacency matrix of a hexagonal system and the number of matchings are obtained. (~) 1998 Elsevier Science B.V. All rights reserved

A linear programming (LP) approach is proposed for the weighted graph matching problem. A linear program is obtained by formulating the graph matching problem in L1 norm and then transforming the resulting quadratic optimization problem to a linear one. The linear program is solved using a Simplex-based algorithm. Then, approximate 0-1 integer solutions are obtained by applying the Hungarian me...

We introduce a general class of learning algorithms, regret-matching algorithms, and a regret-based framework for analyzing their performance in online decision problems. Our analytic framework is based on a set Φ of transformations over the set of actions. Specifically, we calculate a Φ-regret vector by comparing the average reward obtained by an agent over some finite sequence of rounds to th...

In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete even when restricted to bipartite graphs. It has been proved that Matching Cut is polynomially solvable for graphs of diameter two. In this paper, we show that, for any fixed integer d ≥ 4, Matching Cut is NP-comp...

In a weighted undirected graph, a matching is said to be α-robust if for all p, the total weight of its heaviest p edges is at least α times the maximum weight of a p-matching in the graph. Here a p-matching is a matching with at most p edges. In 2002, Hassin and Rubinstein [5] showed that every graph has a 1 √ 2 -robust matching and it can be found by k-th power algorithm in polynomial time. I...