Abstract. An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ( F ( into n pieces F,, 1 5 i 5 n, each of length ( F, 1 = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths ( F, 1 is (n/m). L. Since n/m can be chosen to be close to I, the IDA is space eflicient. IDA has numerous applications to secure and reliable storage of information in computer networks and even on single disks, to fault-tolerant and efficient transmission of information in networks, and to communi-cations between processors in parallel computers. For the latter problem provably time-efftcient and highly fault-tolerant routing on the n-cube is achieved, using just constant size buffers. Categories and Subject Descriptors: E.4 [Coding and Information Theory]: nonsecret encoding schemes

We propose a new approach for constructing P2P networks based on a dynamic decomposition of a continuous space into cells corresponding to processors. We demonstrate the power of these design rules by suggesting two new architectures, one for DHT (Distributed Hash Table) and the other for dynamic expander networks. The DHT network, which we call Distance Halving, allows logarithmic routing and load, while preserving constant degrees. Our second construction builds a network that is guaranteed to be an expander. The resulting topologies are simple to maintain and implement. Their simplicity makes it easy to modify and add protocols. We show it is possible to reduce the dilation and the load of the DHT with a small increase of the degree. We present a provably good protocol for relieving hot spots and a construction with high fault tolerance. Finally we show that, using our approach, it is possible to construct any family of constant degree graphs in a dynamic environment, though with worst parameters. Therefore we expect that more distributed data structures could be designed and implemented in a dynamic environment.

The main objective of this sequel is to solve the out-of-sequence problem that occurs in the load balanced Birkhoff-von Neumann switch with one-stage buffering. We do this by adding a load-balancing buffer in front of the first stage and a resequencing-and-output buffer after the second stage. Moreover, packets are distributed at the first stage according to their flows, instead of their arrival times in Part I. In this paper, we consider multicasting ows with two types of scheduling policies: the First Come First Served (FCFS) policy and the Earliest Deadline First (EDF) policy. The FCFS policy requires a jitter control mechanism in front of the second stage to ensure proper ordering of the traffic entering the second stage. For the EDF scheme, there is no need for jitter control. It uses the departure times of the corresponding FCFS output-buffered switch as deadlines and schedules packets according to their deadlines. For both policies, we show that the end-to-end delay through our multistage switch is bounded above by the sum of the delay from the corresponding FCFS output-buffered switch and a constant that only depends on the size of the switch and the number of multicasting flows supported by the switch.

Chernoff--Hoeffding bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables. We present a simple technique which gives slightly better bounds than these, and which more importantly requires only limited independence among the random variables, thereby importing a variety of standard results to the case of limited independence for free. Additional methods are also presented, and the aggregate results are sharp and provide a better understanding of the proof techniques behind these bounds. They also yield improved bounds for various tail probability distributions and enable improved approximation algorithms for jobshop scheduling. The "limited independence" result implies that a reduced amount of randomness and weaker sources of randomness are sufficient for randomized algorithms whose analyses use the Chernoff--Hoeffding bounds, e.g., the analysis of randomized algorithms for random sampling and oblivious packet routi...

This paper presents a general paradigm for the design of packet routing algorithms for fixed-connection networks. Its basis is a randomized on-line algorithm for scheduling any set of N packets whose paths have congestion c on any bounded-degree leveled network with depth L in O(c + L + log N) steps, using constant-size queues. In this paradigm, the design of a routing algorithm is broken into three parts: (1) showing that the underlying network can emulate a leveled network, (2) designing a path selection strategy for the leveled network, and (3) applying the scheduling algorithm. This strategy yields randomized algorithms for routing and sorting in time proportional to the diameter for meshes, butterflies, shuffle-exchange graphs, multidimensional arrays, and hypercubes. It also leads to the construction of an area-universal network: an N-node network with area Θ(N) that can simulate any other network of area O(N) with slowdown O(log N).

ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately log n= log log n with high probability. Now suppose instead that the balls are placed sequentially, and each ball is placed in the least loaded of d 2 bins chosen independently and uniformly at random. Azar, Broder, Karlin, and Upfal showed that in this case, the maximum load is log log n= log d + (1) with high probability [ABKU99]. The important implication of this result is that even a small amount of choice can lead to drastically different results in load balancing. Indeed, having just two random choices (i.e.,...

It is now more than a quarter of a century since researchers started publishing papers on mapping strategies for distributing computation across the computation resource of multiprocessor systems. There exists a large body of literature on the subject, but there is no commonly-accepted framework whereby results in the field can be compared. Nor is it always easy to assess the relevance of a new result to a particular problem. Furthermore, changes in parallel computing technology have made some of the earlier work of less relevance to current multiprocessor systems. Versions of the mapping problem are classified, and research in the field is considered in terms of its relevance to the problem of programming currently available hardware in the form of a distributed memory multiple instruction stream multiple data stream computer: a multicomputer.

Shortest path routing protocols may suffer from congestion due to the use of a single shortest path between a source and a destination. The goal of our work is to first understand how links become overloaded in an IP backbone, and then to explore if the routing protocol, -- either in its existing form, or in some enhanced form could be made to respond immediately to overload and reduce the likelihood of its occurrenc Our method is to use extensive measurements of Sprint backbone network, measuring 138 links between September 2000 and June 2001. We find that since the backbone is designed to be overprovisioned, link overload is rare, and when it occurs, 80% of the time it is caused due to link failures. Furthermore, we find that when a link is overloaded, few (if any) other links in the network are also overloaded This suggests that deflecting packets to less utilized alternate paths could be an effective method for tackling overload. We analytically derive the condition that a network, which has multiple equal length shortest paths between every pair of nodes (as is common in the highly meshed backbone networks) can provide for loop-free deflection paths if all the link weights are within a ratio 1 + 1/(d-1)of each other; where d is the diameter of the network. Based on our measurements, the nature of the backbone topology and the careful use of link weights, we propose a deflection routing algorithm to tackle link overload where each node makes local decisions. Simulations suggest that this can be a simple and efficient way to overcome link overload without requiring any changes to the routing protocol. Link Failure, Traffic Engineering.

We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peer-to-peer 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 peer-to-peer system where nodes are embedded at grid points in a simple metric space: a one-dimensional 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 power-law 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.

Fat-trees are a class of routing networks for hardware-efficient parallel computation. This paper presents a randomized algorithm for routing messages on a fat-tree. 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 fat-tree 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 off-line 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 fat-trees are universal routing networks. Specifically, we prove that any routing network can be efficiently simulated by a fat-tree of comparable hardware cost. 1 Introduction Fat-trees constitute...