160 research outputs found

    A Study of Arc Strong Connectivity of Digraphs

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    My dissertation research was motivated by Matula and his study of a quantity he called the strength of a graph G, kappa\u27( G) = max{lcub}kappa\u27(H) : H G{rcub}. (Abstract shortened by ProQuest.)

    Algorithms for Dense Graphs and Networks on the Random Access Computer

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    On coding labeled trees

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    Trees are probably the most studied class of graphs in Computer Science. In this thesis we study bijective codes that represent labeled trees by means of string of node labels. We contribute to the understanding of their algorithmic tractability, their properties, and their applications. The thesis is divided into two parts. In the first part we focus on two types of tree codes, namely Prufer-like codes and Transformation codes. We study optimal encoding and decoding algorithms, both in a sequential and in a parallel setting. We propose a unified approach that works for all Prufer-like codes and a more generic scheme based on the transformation of a tree into a functional digraph suitable for all bijective codes. Our results in this area close a variety of open problems. We also consider possible applications of tree encodings, discussing how to exploit these codes in Genetic Algorithms and in the generation of random trees. Moreover, we introduce a modified version of a known code that, in Genetic Algorithms, outperform all the other known codes. In the second part of the thesis we focus on two possible generalizations of our work. We first take into account the classes of k-trees and k-arch graphs (both superclasses of trees): we study bijective codes for this classes of graphs and their algorithmic feasibility. Then, we shift our attention to Informative Labeling Schemes. In this context labels are no longer considered as simple unique node identifiers, they rather convey information useful to achieve efficient computations on the tree. We exploit this idea to design a concurrent data structure for the lowest common ancestor problem on dynamic trees. We also present an experimental comparison between our labeling scheme and the one proposed by Peleg for static trees

    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

    An extensive English language bibliography on graph theory and its applications

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    Bibliography on graph theory and its application

    Routing on the Channel Dependency Graph:: A New Approach to Deadlock-Free, Destination-Based, High-Performance Routing for Lossless Interconnection Networks

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    In the pursuit for ever-increasing compute power, and with Moore's law slowly coming to an end, high-performance computing started to scale-out to larger systems. Alongside the increasing system size, the interconnection network is growing to accommodate and connect tens of thousands of compute nodes. These networks have a large influence on total cost, application performance, energy consumption, and overall system efficiency of the supercomputer. Unfortunately, state-of-the-art routing algorithms, which define the packet paths through the network, do not utilize this important resource efficiently. Topology-aware routing algorithms become increasingly inapplicable, due to irregular topologies, which either are irregular by design, or most often a result of hardware failures. Exchanging faulty network components potentially requires whole system downtime further increasing the cost of the failure. This management approach becomes more and more impractical due to the scale of today's networks and the accompanying steady decrease of the mean time between failures. Alternative methods of operating and maintaining these high-performance interconnects, both in terms of hardware- and software-management, are necessary to mitigate negative effects experienced by scientific applications executed on the supercomputer. However, existing topology-agnostic routing algorithms either suffer from poor load balancing or are not bounded in the number of virtual channels needed to resolve deadlocks in the routing tables. Using the fail-in-place strategy, a well-established method for storage systems to repair only critical component failures, is a feasible solution for current and future HPC interconnects as well as other large-scale installations such as data center networks. Although, an appropriate combination of topology and routing algorithm is required to minimize the throughput degradation for the entire system. This thesis contributes a network simulation toolchain to facilitate the process of finding a suitable combination, either during system design or while it is in operation. On top of this foundation, a key contribution is a novel scheduling-aware routing, which reduces fault-induced throughput degradation while improving overall network utilization. The scheduling-aware routing performs frequent property preserving routing updates to optimize the path balancing for simultaneously running batch jobs. The increased deployment of lossless interconnection networks, in conjunction with fail-in-place modes of operation and topology-agnostic, scheduling-aware routing algorithms, necessitates new solutions to solve the routing-deadlock problem. Therefore, this thesis further advances the state-of-the-art by introducing a novel concept of routing on the channel dependency graph, which allows the design of an universally applicable destination-based routing capable of optimizing the path balancing without exceeding a given number of virtual channels, which are a common hardware limitation. This disruptive innovation enables implicit deadlock-avoidance during path calculation, instead of solving both problems separately as all previous solutions
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