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237
Faulttolerant Routing in Peertopeer Systems
, 2003
"... We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peertopeer system. We argue that many existing approaches to this problem can be modeled as the construction of a random graph embedded in a metric space whose points repre ..."
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Cited by 68 (1 self)
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We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peertopeer system. We argue that many existing approaches to this problem can be modeled as the construction of a random graph embedded in a metric space whose points represent resource identifiers, where the probability of a connection between two nodes depends only on the distance between them in the metric space. We study the performance of a peertopeer system where nodes are embedded at grid points in a simple metric space: a onedimensional real line. We prove upper and lower bounds on the message complexity of locating particular resources in such a system, under a variety of assumptions about failures of either nodes or the connections between them. Our lower bounds in particular show that the use of inverse powerlaw distributions in routing, as suggested by Kleinberg [5], is close to optimal. We also give efficient heuristics to dynamically maintain such a system as new nodes arrive and old nodes depart. Finally, we give experimental results that suggest promising directions for future work.
A constantfactor approximation algorithm for packet routing, and balancing local vs. global criteria
 In Proceedings of the ACM Symposium on the Theory of Computing (STOC
, 1997
"... Abstract. We present the first constantfactor approximation algorithm for a fundamental problem: the storeandforward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at the edges are bounded by an absolute constant. Thus, this algorithmbalances a global criterio ..."
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Cited by 57 (4 self)
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Abstract. We present the first constantfactor approximation algorithm for a fundamental problem: the storeandforward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at the edges are bounded by an absolute constant. Thus, this algorithmbalances a global criterion (routing time) with a local criterion (maximum queue size) and shows how to get simultaneous good bounds for both. For this particular problem, approximating the routing time well, even without considering the queue sizes, was open. We then consider a class of such local vs. global problems in the context of covering integer programs and show how to improve the local criterion by a logarithmic factor by losing a constant factor in the global criterion.
Cope: traffic engineering in dynamic networks
 in SIGCOMM ’06: Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
, 2006
"... Traffic engineering plays a critical role in determining the performance and reliability of a network. A major challenge in traffic engineering is how to cope with dynamic and unpredictable changes in traffic demand. In this paper, we propose COPE, a class of traffic engineering algorithms that o ..."
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Cited by 56 (3 self)
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Traffic engineering plays a critical role in determining the performance and reliability of a network. A major challenge in traffic engineering is how to cope with dynamic and unpredictable changes in traffic demand. In this paper, we propose COPE, a class of traffic engineering algorithms that optimize for the expected scenarios while providing a worstcase guarantee for unexpected scenarios. Using extensive evaluations based on real topologies and traffic traces, we show that COPE can achieve efficient resource utilization and avoid network congestion in a wide variety of scenarios.
Routing Networks for Distributed Hash Tables
, 2003
"... Routing topologies for distributed hashing in peertopeer networks are classified into two categories: deterministic and randomized. A general technique for constructing deterministic routing topologies is presented. Using this technique, classical parallel interconnection networks can be adapted ..."
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Cited by 56 (7 self)
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Routing topologies for distributed hashing in peertopeer networks are classified into two categories: deterministic and randomized. A general technique for constructing deterministic routing topologies is presented. Using this technique, classical parallel interconnection networks can be adapted to handle the dynamic nature of participants in peertopeer networks. A unified picture of randomized routing topologies is also presented. Two new protocols are described which improve average latency as a function of outdegree. One of the protocols can be shown to be optimal with high probability. Finally, routing networks for distributed hashing are revisited from a systems perspective and several open design problems are listed.
Randomized Routing on FatTrees
 Advances in Computing Research
, 1996
"... Fattrees are a class of routing networks for hardwareefficient parallel computation. This paper presents a randomized algorithm for routing messages on a fattree. The quality of the algorithm is measured in terms of the load factor of a set of messages to be routed, which is a lower bound on the ..."
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Cited by 55 (11 self)
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Fattrees are a class of routing networks for hardwareefficient parallel computation. This paper presents a randomized algorithm for routing messages on a fattree. The quality of the algorithm is measured in terms of the load factor of a set of messages to be routed, which is a lower bound on the time required to deliver the messages. We show that if a set of messages has load factor on a fattree with n processors, the number of delivery cycles (routing attempts) that the algorithm requires is O(+lg n lg lg n) with probability 1 \Gamma O(1=n). The best previous bound was O( lg n) for the offline problem in which the set of messages is known in advance. In the context of a VLSI model that equates hardware cost with physical volume, the routing algorithm can be used to demonstrate that fattrees are universal routing networks. Specifically, we prove that any routing network can be efficiently simulated by a fattree of comparable hardware cost. 1 Introduction Fattrees constitute...
On the Fault Tolerance of Some Popular BoundedDegree Networks
 SIAM Journal on Computing
, 1992
"... In this paper, we analyze the ability of several boundeddegree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an Nnode butterfly containing N 1\Gammaffl worstcase faults (for any constant ffl ? 0) can emulate a faultfree butterfly ..."
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Cited by 50 (9 self)
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In this paper, we analyze the ability of several boundeddegree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an Nnode butterfly containing N 1\Gammaffl worstcase faults (for any constant ffl ? 0) can emulate a faultfree butterfly of the same size with only constant slowdown. Similar results are proved for the shuffleexchange graph. Hence, these networks become the first connected boundeddegree networks known to be able to sustain more than a constant number of worstcase faults without suffering more than a constantfactor slowdown in performance. We also show that an Nnode butterfly whose nodes fail with some constant probability p can emulate a faultfree version of itself with a slowdown of 2 O(log N) , which is a very slowly increasing function of N . The proofs of these results combine the technique of redundant computation with new algorithms for (packet) routing around faults in hypercubic networks. Tech...
Efficient and robust routing of highly variable traffic
 In Proceedings of Third Workshop on Hot Topics in Networks (HotNetsIII
, 2004
"... ..."
Regional Congestion Awareness for Load Balance in NetworksonChip
 APPEARS IN THE PROCEEDINGS OF THE 14 TH INTERNATIONAL SYMPOSIUM ON HIGHPERFORMANCE COMPUTER ARCHITECTURE
"... Interconnection networksonchip (NOCs) are rapidly replacing other forms of interconnect in chip multiprocessors and systemonchip designs. Existing interconnection networks use either oblivious or adaptive routing algorithms to determine the route taken by a packet to its destination. Despite som ..."
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Cited by 48 (3 self)
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Interconnection networksonchip (NOCs) are rapidly replacing other forms of interconnect in chip multiprocessors and systemonchip designs. Existing interconnection networks use either oblivious or adaptive routing algorithms to determine the route taken by a packet to its destination. Despite somewhat higher implementation complexity, adaptive routing enjoys better fault tolerance characteristics, increases network throughput, and decreases latency compared to oblivious policies when faced with nonuniform or bursty traffic. However, adaptive routing can hurt performance by disturbing any inherent global load balance through greedy local decisions. To improve load balance in adapting routing, we propose Regional Congestion Awareness (RCA), a lightweight technique to improve global network balance. Instead of relying solely on local congestion information, RCA informs the routing policy of congestion in parts of the network beyond adjacent routers. Our experiments show that RCA matches or exceeds the performance of conventional adaptive routing across all workloads examined, with a 16 % average and 71 % maximum latency reduction on SPLASH2 benchmarks running on a 49core CMP. Compared to a baseline adaptive router, RCA incurs a negligible logic and modest wiring overhead.
Routing Permutations on Graphs via Matchings
 SIAM Journal on Discrete Mathematics
, 1994
"... We consider a class of routing problems on connected graphs G. Initially, each vertex v of G is occupied by a “pebble ” which has a unique destination π(v) in G (so that π is a permutation of the vertices of G). It is required to route all the pebbles to their respective destinations by performing a ..."
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Cited by 44 (2 self)
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We consider a class of routing problems on connected graphs G. Initially, each vertex v of G is occupied by a “pebble ” which has a unique destination π(v) in G (so that π is a permutation of the vertices of G). It is required to route all the pebbles to their respective destinations by performing a sequence of moves of the following type: A disjoint set of edges is selected and the pebbles at each edge’s endpoints are interchanged. The problem of interest is to minimize the number of steps required for any possible permutation π. In this paper we investigate this routing problem for a variety of graphs G, including trees, complete graphs, hypercubes, Cartesian products of graphs, expander graphs and Cayley graphs. In addition, we relate this routing problem to certain network flow problems, and to several graph invariants including diameter, eigenvalues and expansion coefficients. 2 1