This study focuses on the routing and Wavelength-Assignment (RWA) problem in wavelength-routed optical WDM networks. Most of the attention is devoted to such networks operating under the wavelength-continuity constraint, in which lightpaths are set up for connection requests between node pairs, and a single lightpath must occupy the same wavelength on all of the links that it spans. In setting up a lightpath, a route must be selected and a wavelength must be assigned to the lightpath. If no wavelength is available for this lightpath on the selected route, then the connection request is blocked. We examine the RWA problem and review various routing approaches and wavelengthassignment approaches proposed in the literature. We also briefly consider the characteristics of wavelength-converted networks (which do not have the wavelength-continuity constraint), and we examine the associated research problems and challenges. Finally, we propose a new wavelengthassignment scheme, called Distributed Relative Capacity Loss (DRCL), which works well in distributed-controlled networks, and we demonstrate the performance of DRCL through simulation. 1

We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques.

We have developed a novel algorithm for cluster analysis that is based on graph theoretic techniques. A similarity graph is defined and clusters in that graph correspond to highly connected subgraphs. A polynomial algorithm to compute them efficiently is presented. Our algorithm produces a clustering with some provably good properties. The application that motivated this study was gene expression analysis, where a collection of cDNAs must be clustered based on their oligonucleotide fingerprints. The algorithm has been tested intensively on simulated libraries and was shown to outperform extant methods. It demonstrated robustness to high noise levels. In a blind test on real cDNA fingerprint data the algorithm obtained very good results. Utilizing the results of the algorithm would have saved over 70% of the cDNA sequencing cost on that data set. 1 Introduction Cluster analysis seeks grouping of data elements into subsets, so that elements in the same subset are in some sense more cl...

Abstract not found

Abstract not found

Many applications, like the retrieval of information from the WWW, require or are improved by the detection of sets of closely related vertices in graphs. Depending on the application, many approaches are possible. In this paper we present a purely graph-theoretical approach, independent of the represented data. Based on the edge-connectivity of subgraphs, a tree of subgraphs is constructed, such that the children of a node are pairwise disjoint and contained in their parent. We describe a polynomial algorithm for the construction of the tree and present two heuristics, constructing the correct result in signi cantly decreased time. Furthermore we give a short description of possible applications in the elds of information retrieval, clustering and graph drawing. 1.

Abstract. We present in this paper a method to discover the set of webpages contained in a logical website, based on the link structure of the Web graph. Such a method is useful in the context of Web archiving and website importance computation. To identify the boundaries of a website, we combine the use of an online version of the preflow-push algorithm, an algorithm for the maximum flow problem in traffic networks, and of the Markov CLuster (MCL) algorithm. The latter is used on a crawled portion of the Web graph in order to build a seed of initial webpages, a seed which is extended using the former. Experiments on subsites of the INRIA Website are described. 1

In this paper, we study properties for the structure of an undirected graph that is not 4-vertex-connected. We also study the evolution of this structure when an edge is added to optimally increase the vertex-connectivity of the underlying graph. Several properties reported here can be extended to the case of a graph that is not k-vertex- connected, for an arbitrary k. Using properties obtained here, we solve the problem of finding a smallest set of edges whose addition 4-vertex-connects an undirected graph. This is a fundamental problem in graph theory and has applications in network reliability and in statistical data security. We give an O(n \Delta log n + m)-time algorithm for finding a set of edges with the smallest cardinality whose addition 4-vertex-connects an undirected graph, where n and m are the number of vertices and edges in the input graph, respectively. This is the first polynomial time algorithm for this problem when the input graph is not 3-vertex-connecte...

The paradigm adopted by classical Web search engines to output the results of a query is often inadequate. It typically consists of a ranked list of URLs, which may be very long and difficult to browse for the interested user. Recently, a lot of attention has been devoted to the design of Web meta-search clustering engines. These systems support the user by grouping the URLs returned by a search engine into distinct semantic categories, which are organized in a hierarchy; each category is properly labeled with a sentence that reflects its topics. However, even the most effective Web meta-search engines usually end-up by presenting many “meaningful ” categories together with a few “inexpressive ” categories on some specific queries. In this paper we describe a novel topology-driven approach to the design of a Web meta-search clustering engine. By this approach the set of URLs is modeled as a suitable graph and the hierarchy of categories is obtained by variants of classical graph-clustering algorithms. The topologydriven approach turns out to be comparable with traditional text-based strategies for the definition of the cluster hierarchy. In addition, our approach makes it natural to use graph visualization techniques to support the user in handling inexpressive labels. Namely, categories with inexpressive labels can be visually related to more meaningful ones. 1

. A cut in a graph G is the set of all edges between some set of vertices S and its complement S = V (G) \Gamma S. A cut-cover of G is a collection of cuts whose union is E(G) and the total size of a cut-cover is the sum of the number of edges of the cuts in the cover. The cut-cover size of a graph G, denoted by cs(G), is the minimum total size of a cut-cover of G. We will give general bounds on cs(G), find sharp bounds for classes of graphs such as 4-colorable graphs and random graphs and prove a Nordhaus-Gaddum type result. We close with a list of open problems. 1. The cut-cover problem Covering the edges of a graph by subgraphs from a given family of graphs, like cliques, matchings, trees, or cycles, is one of the basic themes in graph theory (see [Py] for a survey of results). Erdos, Goodman and P'osa [EGP] showed that the edges of every graph on n vertices can be covered by bn 2 =4c cliques and the balanced complete bipartite graph shows that this is best possible. It can als...