We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph G = (A ∪ P , E), where A denotes a set of applicants, P is a set of posts, and there are ranks on edges which denote the preferences of applicants over posts. A matching M in G is called rank-maximal if it matches the maximum number of applican...

In 1], the authors described the design of the AN2 switch which supports high-performance distributed computing. The switch's operation is based on the parallel iterative matching algorithm to nd a maximal matching between the inputs and the outputs of the switch. The number of iterations needed to nd a maximal matching in their algorithm is N in the worst case, and of time complexity O(log N) ...

Let k be a positive integer, a subset Q of the set of vertices of a graph G is k-dependent in G if each vertex of Q has no more than k neighbours in Q. We present a parallel algorithm which computes a maximal k-dependent set in a graph on n nodes in time O(log 4 n) on an EREW PRAM with O(n 2) processors. In this way, we establish the membership of the problem of constructing a maximal k-depende...

We investigate the use of a background knowledge ontology in ontology matching. We conducted experiments on matching two medical ontologies using a third extensive one as background knowledge, and compare the results with directly matching the two ontologies. Our results indicate that using background knowledge, in particular the exploitation of its structure, has enormous benefits on the match...

The regularity of an edge ideal of a finite simple graph G is at least the induced matching number of G and is at most the minimum matching number of G. If G possesses a dominating induced matching, i.e., an induced matching which forms a maximal matching, then the induced matching number of G is equal to the minimum matching number of G. In the present paper, from viewpoints of both combinator...

In this paper we present a new width measure for a tree decomposition, minor-matching hypertree width, μ-tw, for graphs and hypergraphs, such that bounding the width guarantees that set of maximal independent sets has a polynomially-sized restriction to each decomposition bag. The relaxed conditions of the decomposition allow a much wider class of graphs and hypergraphs of bounded width compare...

We show an O(1.344) = O(2) algorithm for edge-coloring an n-vertex graph using three colors. Our algorithm uses polynomial space. This improves over the previous, O(2) algorithm of Beigel and Eppstein [1]. We apply a very natural approach of generating inclusion-maximal matchings of the graph. The time complexity of our algorithm is estimated using the “measure and con-

G is a well-covered graph provided all its maximal stable sets are of the same size (Plummer, 1970). S is a local maximum stable set of G, and we denote by S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S. In 2002 we have proved that Ψ(G) is a greedoid for every forest G. The bipartite graphs and the trianglefree graphs, whose famil...

1 Approximation Algorithms Any known algorithm that finds the solution to an NP-hard optimization problem has exponential running time. However, sometimes polynomial time algorithms exist which find a " good " solution instead of an optimum solution. Given a minimization problem and an approximation algorithm, we can evaluate the algorithm as follows. First, we find a lower bound on the optimum...

In this paper we study some combinatorial properties of a class of languages that represent sets of words occurring in a text S up to some errors. More precisely, we consider sets of words that occur in a text S with k mismatches in any window of size r . The study of this class of languages mainly focuses both on a parameter, called repetition index, and on the set of the minimal forbidden wor...