139 research outputs found

    Efficient routing schemes for multiple broadcasts in hypercubes

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    "February 1990/Revised June 1990."--Cover. Cover title.Includes bibliographical references (p. 36-37).Research supported by the NSF. ECS-8552419 Research supported by Bellcore, Inc. and Du Pont. Research supported by the ARO. DAAL03-86-K-0171 Research supported by a fellowship from the Vinton Hayes Fund.George D. Stamoulis and John N. Tsitsiklis

    The spectra of Manhattan street networks

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    AbstractThe multidimensional Manhattan street networks constitute a family of digraphs with many interesting properties, such as vertex symmetry (in fact they are Cayley digraphs), easy routing, Hamiltonicity, and modular structure. From the known structural properties of these digraphs, we determine their spectra, which always contain the spectra of hypercubes. In particular, in the standard (two-dimensional) case it is shown that their line digraph structure imposes the presence of the zero eigenvalue with a large multiplicity

    The spectra of Manhattan street networks

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    The multidimensional Manhattan street networks constitute a family of digraphs with many interesting properties, such as vertex symmetry (in fact they are Cayley digraphs), easy routing, Hamiltonicity, and modular structure. From the known structural properties of these digraphs, we determine their spectra, which always contain the spectra of hypercubes. In particular, in the standard (two-dimensional) case it is shown that their line digraph structure imposes the presence of the zero eigenvalue with a large multiplicity

    Neighbourhood Broadcasting in Hypercubes

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    International audienceIn the broadcasting problem, one node needs to broadcast a message to all other nodes in a network. If nodes can only communicate with one neighbor at a time, broadcasting takes at least log2N\lceil \log_2 N \rceil rounds in a network of NN nodes. In the neighborhood broadcasting problem, the node that is broadcasting needs to inform only its neighbors. In a binary hypercube with NN nodes, each node has log2N\log_2 N neighbors, so neighborhood broadcasting takes at least log2log2(N+1)\lceil \log_2 \log_2 (N+1) \rceil rounds. In this paper, we present asymptotically optimal neighborhood broadcast protocols for binary hypercubes

    Hypercube-Based Topologies With Incremental Link Redundancy.

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    Hypercube structures have received a great deal of attention due to the attractive properties inherent to their topology. Parallel algorithms targeted at this topology can be partitioned into many tasks, each of which running on one node processor. A high degree of performance is achievable by running every task individually and concurrently on each node processor available in the hypercube. Nevertheless, the performance can be greatly degraded if the node processors spend much time just communicating with one another. The goal in designing hypercubes is, therefore, to achieve a high ratio of computation time to communication time. The dissertation addresses primarily ways to enhance system performance by minimizing the communication time among processors. The need for improving the performance of hypercube networks is clearly explained. Three novel topologies related to hypercubes with improved performance are proposed and analyzed. Firstly, the Bridged Hypercube (BHC) is introduced. It is shown that this design is remarkably more efficient and cost-effective than the standard hypercube due to its low diameter. Basic routing algorithms such as one to one and broadcasting are developed for the BHC and proven optimal. Shortcomings of the BHC such as its asymmetry and limited application are clearly discussed. The Folded Hypercube (FHC), a symmetric network with low diameter and low degree of the node, is introduced. This new topology is shown to support highly efficient communications among the processors. For the FHC, optimal routing algorithms are developed and proven to be remarkably more efficient than those of the conventional hypercube. For both BHC and FHC, network parameters such as average distance, message traffic density, and communication delay are derived and comparatively analyzed. Lastly, to enhance the fault tolerance of the hypercube, a new design called Fault Tolerant Hypercube (FTH) is proposed. The FTH is shown to exhibit a graceful degradation in performance with the existence of faults. Probabilistic models based on Markov chain are employed to characterize the fault tolerance of the FTH. The results are verified by Monte Carlo simulation. The most attractive feature of all new topologies is the asymptotically zero overhead associated with them. The designs are simple and implementable. These designs can lead themselves to many parallel processing applications requiring high degree of performance

    Routing and caching on DHTS

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    L'obiettivo della tesi e' quello di analizzare i principali meccanismi di caching e routing implementati oggigiorno nelle DHT piu' utilizzate. In particolare, la nostra analisi mostra come tali meccanismi siano sostanzialmente inefficaci nel garantire un adeguato load balancing tra i peers; le principali cause di questo fenomeno sono individuate nella struttura, eccessivamente rigida, adottata dalle DHT e nella mancanza di correlazione tra meccanismi di routing e di caching. Viene quindi proposto un diverso overlay, organizzato in base a una struttura ipercubica, che permetta di adottare un algoritmo di routing piu' flessibile e di sviluppare due meccanismi di caching e routing strettamente interconnessi. In particolare, l'overlay ottenuto riesce a garantire che ogni nodo subisca un carico al piu' costante, con una taglia di cache costante e una complessita' di routing polilogaritmica nel caso peggior

    Heuristics for Message Broadcasting in Arbitrary Networks

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    With the increasing popularity of interconnection networks, efficient information dissemination has become a popular research area. Broadcasting is one of the information dissemination primitives. Finding the optimal broadcasting scheme for any originator in an arbitrary network has been proved to be an NP-Hard problem. In this thesis, two new heuristics that generate broadcast schemes in arbitrary networks are presented. Both of them have O(|E|) time complexity. Moreover, in the broadcast schemes generated by the heuristics, each vertex in the network receives the message via a shortest path. Based on computer simulations of these heuristics in some commonly used topologies and network models, and comparing the results with the best existing heuristics, we conclude that the new heuristics show comparable performances while having lower complexity

    New Heuristic for Message Broadcasting in Arbitrary Networks

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    Efficient information dissemination in interconnection networks is a key research area because of the major role it plays in the modern interconnected world. A vast number of topics ranging from distributed computing to Internet communication rely on efficient information dissemination. Broadcasting is one of the information dissemination primitives. The minimum broadcast time problem in arbitrary networks has been examined since the 1970s. Finding an optimal broadcasting scheme for any originator in an arbitrary network has been proved to be an NP-Hard problem. In the current thesis, a new heuristic that generates broadcast schemes in arbitrary networks is presented. The heuristic has O(|E|log|V|) time complexity, where V is the set of nodes and E is the set of the links of the network. Computer simulations in some commonly used topologies and network models show that compared to the existing heuristics the new heuristic shows better performance in some network models, and comparable performance in other network models, while having a low complexity similar to the best existing heuristics. Another advantage of the new heuristic is that approximately one half of the vertices receive the message via a shortest path from the broadcast originator, while the rest of the vertices receive the message via a path at most three hops longer

    A Black Hole Attack Model for Reactive Ad-Hoc Protocols

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    Net-Centric Warfare places the network in the center of all operations, making it a critical resource to attack and defend during wartime. This thesis examines one particular network attack, the Black Hole attack, to determine if an analytical model can be used to predict the impact of this attack on ad-hoc networks. An analytical Black Hole attack model is developed for reactive ad-hoc network protocols DSR and AODV. To simplify topology analysis, a hypercube topology is used to approximate ad-hoc topologies that have the same average node degree. An experiment is conducted to compare the predicted results of the analytical model against simulated Black Hole attacks on a variety of ad-hoc networks. The results show that the model describes the general order of growth in Black Hole attacks as a function of the number of Black Holes in a given network. The model accuracy maximizes when both the hypercube approximation matches the average degree and number of nodes of the ad-hoc topology. For this case, the model falls within the 95% confidence intervals of the estimated network performance loss for 17 out of 20 measured scenarios for AODV and 7 out of 20 for DSR

    Efficient All-to-All Collective Communication Schedules for Direct-Connect Topologies

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    The all-to-all collective communications primitive is widely used in machine learning (ML) and high performance computing (HPC) workloads, and optimizing its performance is of interest to both ML and HPC communities. All-to-all is a particularly challenging workload that can severely strain the underlying interconnect bandwidth at scale. This is mainly because of the quadratic scaling in the number of messages that must be simultaneously serviced combined with large message sizes. This paper takes a holistic approach to optimize the performance of all-to-all collective communications on supercomputer-scale direct-connect interconnects. We address several algorithmic and practical challenges in developing efficient and bandwidth-optimal all-to-all schedules for any topology, lowering the schedules to various backends and fabrics that may or may not expose additional forwarding bandwidth, establishing an upper bound on all-to-all throughput, and exploring novel topologies that deliver near-optimal all-to-all performance
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