26 research outputs found

    A Parallel Algorithm for Computing Minimum Spanning Trees

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    We present a simple and implementable algorithm that computes a minimum spanning tree of an undirected weighted graph G = (V, E) of n = |V| vertices and m = |E| edges on an EREW PRAM in O(log 3=2 n) time using n+m processors. This represents a substantial improvement in the running time over the previous results for this problem using at the same time the weakest of the PRAM models. It also implies the existence of algorithms having the same complexity bounds for the EREW PRAM, for connectivity, ear decomposition, biconnectivity, strong orientation, st-numbering and Euler tours problems

    Robust network computation

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    Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 91-98).In this thesis, we present various models of distributed computation and algorithms for these models. The underlying theme is to come up with fast algorithms that can tolerate faults in the underlying network. We begin with the classical message-passing model of computation, surveying many known results. We give a new, universally optimal, edge-biconnectivity algorithm for the classical model. We also give a near-optimal sub-linear algorithm for identifying bridges, when all nodes are activated simultaneously. After discussing some ways in which the classical model is unrealistic, we survey known techniques for adapting the classical model to the real world. We describe a new balancing model of computation. The intent is that algorithms in this model should be automatically fault-tolerant. Existing algorithms that can be expressed in this model are discussed, including ones for clustering, maximum flow, and synchronization. We discuss the use of agents in our model, and give new agent-based algorithms for census and biconnectivity. Inspired by the balancing model, we look at two problems in more depth.(cont.) First, we give matching upper and lower bounds on the time complexity of the census algorithm, and we show how the census algorithm can be used to name nodes uniquely in a faulty network. Second, we consider using discrete harmonic functions as a computational tool. These functions are a natural exemplar of the balancing model. We prove new results concerning the stability and convergence of discrete harmonic functions, and describe a method which we call Eulerization for speeding up convergence.by David Pritchard.M.Eng

    Algorithms for Graph Connectivity and Cut Problems - Connectivity Augmentation, All-Pairs Minimum Cut, and Cut-Based Clustering

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    We address a collection of related connectivity and cut problems in simple graphs that reach from the augmentation of planar graphs to be k-regular and c-connected to new data structures representing minimum separating cuts and algorithms that smoothly maintain Gomory-Hu trees in evolving graphs, and finally to an analysis of the cut-based clustering approach of Flake et al. and its adaption to dynamic scenarios

    Recent Advances in Fully Dynamic Graph Algorithms

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    In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms

    The many faces of planarity : matching, augmentation, and embedding algorithms for planar graphs

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    36th International Symposium on Theoretical Aspects of Computer Science: STACS 2019, March 13-16, 2019, Berlin, Germany

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