Authors propose several approaches for increasing performance of multiplicative inversion algorithm in binary fields based on Extended Euclidean Algorithm (EEA). First approach is based on Extended Euclidean Algorithm specificity: either invariant polynomial v remains intact or swaps with invariant polynomial u . It makes it possible to avoid necessity of polynomial v degree computing. The seco...

Whereas matching in Description Logics is now relatively well-investigated, there are only very few formal results on matching under additional side conditions, though these side conditions were already present in the original paper by Borgida and McGuinness introducing matching in DLs. The present paper closes this gap for the DL ALN and its sublanguages: matching under subsumption conditions ...

Roots of graph polynomials such as the characteristic polynomial, the chromatic polynomial, the matching polynomial, and many others are widely studied. In this paper we examine to what extent the location of these roots refl ects the graph theoretic properties of the underlying graph. (Joint work with E. Ravve and N. Blanchard) Johann (János) A. Makowsky is a Hungarian born and naturalized Swi...

We consider a strategic game with two classes of confronting randomized players on a graph G(V,E): ν attackers, each choosing vertices and wishing to minimize the probability of being caught, and a defender, who chooses edges and gains the expected number of attackers it catches. The Price of Defense is the worst-case ratio, over all Nash equilibria, of the optimal gain of the defender over its...

Matchings in graphs correspond to independent sets in the corresponding line graphs. Line graphs are an important subclass of claw-free graphs. Hence studying independence polynomials of claw-free graphs is a natural extension of studying matching polynomials of graphs. We extend a result of Bayati et.al. showing a fully polynomial time approximation scheme (FPTAS) for computing the independenc...

We present a new algorithm for solving the real roots of a bivariate polynomial system R 1⁄4 ff ðx; yÞ; gðx; yÞg with a finite number of solutions by using a zero-matching method. The method is based on a lower bound for the bivariate polynomial system when the system is non-zero. Moreover, the multiplicities of the roots of R 1⁄4 0 can be obtained by the associated quotient ring technique and ...

In an instance G = (A∪B,E) of the stable marriage problem with strict and possibly incomplete preference lists, a matchingM is popular if there is no matchingM ′ where the vertices that prefer M ′ to M outnumber those that prefer M to M ′. All stable matchings are popular and there is a simple linear time algorithm to compute a maximum-size popular matching. More generally, what we seek is a mi...

Suppose that G is a simple graph. We prove that if G contains a small number of cycles of even length then the matching polynomial of G can be expressed in terms of the characteristic polynomials of the skew adjacency matrix A(G) of an arbitrary orientation G of G and the minors of A(G). In addition to a formula previously discovered by Godsil and Gutman, we obtain a different formula for the m...

A distance-regular graph of diameter d has 2d intersection numbers that determinemany properties of graph (e.g., its spectrum). We show that the first six coefficients of the matching polynomial of a distance-regular graph can also be determined from its intersection array, and that this is the maximum number of coefficients so determined. Also, the converse is true for distance-regular graphs ...