Fast Computation of Small Cuts via Cycle Space Sampling

We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the cycle space identifies the cuts of a graph. This leads to simple new linear-time sequential algorithms for finding all cut edges and cut pairs (a set of 2 edges that form a cut) of a graph. In the model of distributed computing in a graph G=(V, E) with O(log V)-bit messages, our approach yields faster algorithms for several problems. The diameter of G is denoted by Diam, and the maximum degree by Delta. We obtain simple O(Diam)-time distributed algorithms to find all cut edges, 2-edge-connected components, and cut pairs, matching or improving upon previous time bounds. Under natural conditions these new algorithms are universally optimal --- i.e. a Omega(Diam)-time lower bound holds on every graph. We obtain a O(Diam+Delta/log V)-time distributed algorithm for finding cut vertices; this is faster than the best previous algorithm when Delta, Diam = O(sqrt(V)). A simple extension of our work yields the first distributed algorithm with sub-linear time for 3-edge-connected components. The basic distributed algorithms are Monte Carlo, but they can be made Las Vegas without increasing the asymptotic complexity. In the model of parallel computing on the EREW PRAM our approach yields a simple algorithm with optimal time complexity O(log V) for finding cut pairs and 3-edge-connected components.Comment: Previous version appeared in Proc. 35th ICALP, pages 145--160, 200

Finding 3-edge-connected components in parallel

A parallel algorithm for finding 3-edge-connected components of an undirected graph on a CRCW PRAM is presented. The time and work complexity of this algorithm is O(logn) and O((m+n)loglogn), respectively, where n is the number of vertices and m is the number of edges in the input graph. The algorithm is based on ear decomposition and reduction of 3-edge-connectivity to 1-vertex-connectivity. This is the first 3-edge-connected component algorithm of a parallel model

A study of word frequency in written Urdu

Performance on word processing tasks is known to be influenced by the frequency with which words occur in a language. Large and robust effects of word frequency occur across languages and the processes thought to be sensitive to word frequency are considered fundamentally important characteristics of the mental lexicon (Monsell, 1991). A major role of these frequency sensitive processes is embedded in most models of word recognition. Indeed the adequacy of models of word recognition hinges upon their ability to explain this pervasive effect. Thus, it is imperative to understand the effects of frequency in the processing of any language under study and it is crucial that this ubiquitous effect be controlled when examining less robust and influential effects. To my knowledge, no frequency data exists for Urdu, a South Asian language of Perso-Arabic origin. My ultimate goal is to study language processing in native and bilingual speakers of Urdu, and before I embark on this endeavour, it is essential to provide a word frequency database for the language. I have thus constructed a word frequency database for written Urdu. The frequency counts from this database will help psycholinguists and cognitive psychologists conduct and control future studies on the mental lexicon using Urdu. The credibility of this database has been demonstrated by conducting a lexical decision task using words from this database. A frequency effect was obtained which not only indicated that this database is a valid research tool, but also replicated the robust word frequency effect for Urdu.Dept. of Psychology. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2006 .K43. Source: Masters Abstracts International, Volume: 45-01, page: 0485. Thesis (M.A.)--University of Windsor (Canada), 2006

A study of three-edge connectivity algorithms - Refinement and implementation

There are quite a number of linear algorithms to compute 3-edge connected components of a multi-graph. In this thesis, we study the three most efficient algorithms and exclude other algorithms that are obviously inferior as they use different types of transformation in multiple phases. We present a data structure model for cut-pair deletion in order to save space and to be able to handle larger input sizes on a platform. Using complexity arguments we also present a modification to one of the three algorithms that does not look for cut-pairs. We then show through our experimental results that this algorithm and another one that does not distinguish between cut-pairs have the fastest execution time, and each of them is better than the other for some cases. To the best of our knowledge, till now, there is no such an effort to show how the performance of the algorithms varies as the type and the size of given graph changes. Correctness proofs of the proposed way for cut-pair deletion and the modification are presented as well

A Distributed Algorithm for Finding Separation Pairs in a Computer Network

One of the main problems in graph theory is graph connectivity which is often studied for network reliability problems.It can be studied from two aspects, vertex-connectivity and edge-connectivity. Vertex connectivity is the smallest number of vertices whose deletion will cause a connected graph to be disconnected. We focus our work on finding separation pairs of a graph which is the set of pairs of vertices that deleting them would disconnect a graph. Finding separation pairs can be used in solving vertex-connectivity problem and finding the triconnected components of the graph. The algorithms presented during the past are non-linear or if linear, very complicated. This work is based on Tarjan and Hopcroft\u27s paper which uses Depth-First Search and finds the separation pairs in linear time. Our goal is to present an algorithm that finds the separation pairs in an asynchronous distributed computer network using distributed Depth-First search (DDFS)