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50
Mercury: Supporting scalable multiattribute range queries
 In SIGCOMM
, 2004
"... This paper presents the design of Mercury, a scalable protocol for supporting multiattribute rangebased searches. Mercury differs from previous rangebased query systems in that it supports multiple attributes as well as performs explicit load balancing. Efficient routing and load balancing are imp ..."
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Cited by 283 (6 self)
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This paper presents the design of Mercury, a scalable protocol for supporting multiattribute rangebased searches. Mercury differs from previous rangebased query systems in that it supports multiple attributes as well as performs explicit load balancing. Efficient routing and load balancing are implemented using novel lightweight sampling mechanisms for uniformly sampling random nodes in a highly dynamic overlay network. Our evaluation shows that Mercury is able to achieve its goals of logarithmichop routing and nearuniform load balancing. We also show that a publishsubscribe system based on the Mercury protocol can be used to construct a distributed object repository providing efficient and scalable object lookups and updates. By providing applications a rangebased query language to express their subscriptions to object updates, Mercury considerably simplifies distributed state management. Our experience with the design and implementation of a simple distributed multiplayer game built on top of this object management framework shows that indicates that this indeed is a useful building block for distributed applications. Keywords: Range queries, Peertopeer systems, Distributed applications, Multiplayer games 1
Quantized consensus
, 2007
"... We study the distributed averaging problem on arbitrary connected graphs, with the additional constraint that the value at each node is an integer. This discretized distributed averaging problem models several problems of interest, such as averaging in a network with finite capacity channels and loa ..."
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Cited by 64 (0 self)
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We study the distributed averaging problem on arbitrary connected graphs, with the additional constraint that the value at each node is an integer. This discretized distributed averaging problem models several problems of interest, such as averaging in a network with finite capacity channels and load balancing in a processor network. We describe simple randomized distributed algorithms which achieve consensus to the extent that the discrete nature of the problem permits. We give bounds on the convergence time of these algorithms for fully connected networks and linear networks.
Adaptive Packet Routing for Bursty Adversarial Traffic
, 1998
"... One of the central tasks of networking is packetrouting when edge bandwidth is limited. Tremendous progress has been achieved by separating the issue of routing into two conceptual subproblems: path selection and congestion resolution along the selected paths. However, this conceptual separatio ..."
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Cited by 59 (7 self)
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One of the central tasks of networking is packetrouting when edge bandwidth is limited. Tremendous progress has been achieved by separating the issue of routing into two conceptual subproblems: path selection and congestion resolution along the selected paths. However, this conceptual separation has a serious drawback: each packet's path is fixed at the source and cannot be modified adaptively enroute. The problem is especially severe when packet injections are modeled by an adversary, whose goal is to cause "trafficjams".
Local Divergence of Markov Chains and the Analysis of Iterative LoadBalancing Schemes
 IN PROCEEDINGS OF THE 39TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS ’98
, 1998
"... We develop a general technique for the quantitative analysis of iterative distributed load balancing schemes. We illustrate the technique by studying two simple, intuitively appealing models that are prevalent in the literature: the diffusive paradigm, and periodic balancing circuits (or the dimensi ..."
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Cited by 48 (1 self)
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We develop a general technique for the quantitative analysis of iterative distributed load balancing schemes. We illustrate the technique by studying two simple, intuitively appealing models that are prevalent in the literature: the diffusive paradigm, and periodic balancing circuits (or the dimension exchange paradigm). It is well known that such load balancing schemes can be roughly modeled by Markov chains, but also that this approximation can be quite inaccurate. Our main contribution is an effective way of characterizing the deviation between the actual loads and the distribution generated by a related Markov chain, in terms of a natural quantity which we call the local divergence. We apply this technique to obtain bounds on the number of rounds required to achieve coarse balancing in general networks, cycles and meshes in these models. For balancing circuits, we also present bounds for the stronger requirement of perfect balancing, or counting.
Efficient Schemes for Nearest Neighbor Load Balancing
, 1998
"... We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the diffusion type. Within this framework we develop a new optimal polynomial scheme (OPS) which we show to terminate within a finite number m of steps, where m only depends on the graph ..."
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Cited by 46 (13 self)
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We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the diffusion type. Within this framework we develop a new optimal polynomial scheme (OPS) which we show to terminate within a finite number m of steps, where m only depends on the graph and not on the initial load distribution. We show that all existing diffusion load balancing algorithms, including OPS, determine a flow of load on the edges of the graph which is uniquely defined, independent of the method and minimal in the l 2 norm. This result can be extended to edge weighted graphs. The l 2 minimality is achieved only if a diffusion algorithm is used as preprocessing and the real movement of load is performed in a second step. Thus, it is advisable to split the balancing process into the two steps of first determining a balancing flow and afterwards moving the load. We introduce the problem of scheduling a flow and present some first results on its complexity and the ...
Load Balancing Strategies For Distributed Memory Machines
 MultiScale Phenomena and Their Simulation
, 1997
"... Load balancing in large parallel systems with distributed memory is a difficult task often influencing the overall efficiency of applications substantially. A number of efficient distributed load balancing strategies have been developed in the recent years. Although they are currently not generally ..."
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Cited by 29 (1 self)
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Load balancing in large parallel systems with distributed memory is a difficult task often influencing the overall efficiency of applications substantially. A number of efficient distributed load balancing strategies have been developed in the recent years. Although they are currently not generally available as part of parallel operating systems, it is often not difficult to integrate them into applications. This paper gives a classification of different load balancing problems based on application characteristics. For the case of applications out of the field of scientific computing, useful methods are described in more detail.
The Load Rebalancing Problem
 In Proc. of the 15th Ann. ACM Symp. on Parallel Algorithms and Architectures
, 2003
"... In the classical load balancing or multiprocessor scheduling problem, we are given a sequence of jobs of varying sizes and are asked to assign each job to one of the m empty processors. A typical objective is to minimize makespan, the load on the heaviest loaded processor. Since in most real world ..."
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Cited by 25 (0 self)
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In the classical load balancing or multiprocessor scheduling problem, we are given a sequence of jobs of varying sizes and are asked to assign each job to one of the m empty processors. A typical objective is to minimize makespan, the load on the heaviest loaded processor. Since in most real world scenarios the load is a dynamic measure, the initial assignment may be not remain optimal with time. Motivated by such considerations in a variety of systems, we formulate the problem of load rebalancing — given a possibly suboptimal assignment of jobs to processors, relocate a set of the jobs so as to decrease the makespan. Specifically, the goal is to achieve the best possible makespan under the constraint that no more than k jobs are relocated. We also consider a generalization of this problem where there is an arbitrary cost function associated with each job relocation. Since the problem is clearly NPhard, we focus on approximation algorithms. We construct a sophisticated algorithm which achieves a 1.5approximation, with near linear running time. We also show that the problem has a PTAS, resolving the complexity issue. Finally, we investigate the approximability of several extensions of the rebalancing model.
Stability of load balancing algorithms in dynamic adversarial systems
 In Proc. of the 34th ACM Symp. on Theory of Computing (STOC
, 2002
"... Abstract. In the dynamic load balancing problem, we seek to keep the job load roughly evenly distributed among the processors of a given network. The arrival and departure of jobs is modeled by an adversary restricted in its power. Muthukrishnan and Rajaraman (1998) gave a clean characterization of ..."
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Cited by 20 (2 self)
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Abstract. In the dynamic load balancing problem, we seek to keep the job load roughly evenly distributed among the processors of a given network. The arrival and departure of jobs is modeled by an adversary restricted in its power. Muthukrishnan and Rajaraman (1998) gave a clean characterization of a restriction on the adversary that can be considered the natural analogue of a cut condition. They proved that a simple local balancing algorithm proposed by Aiello et. al. (1993) is stable against such an adversary if the insertion rate is restricted to a (1 − ε) fraction of the cut size. They left as an open question whether the algorithm is stable at rate 1. In this paper, we resolve this question positively, by proving stability of the local algorithm at rate 1. Our proof techniques are very different from the ones used by Muthukrishnan and Rajaraman, and yield a simpler proof and tighter bounds on the difference in loads. In addition, we introduce a multicommodity version of this load balancing model, and show how to extend the result to the case of balancing two different kinds of loads at once (obtaining as a corollary a new proof of the 2commodity MaxFlow MinCut Theorem). We also show how to apply the proof techniques to the problem of routing packets in adversarial systems. Awerbuch et. al. (2001) showed that the same load balancing algorithm is stable against an adversary inserting
Delayed path coupling and generating random permutations via distributed stochastic processes
, 1999
"... We analyze various stochastic processes for generating permutations almost uniformly at random in distributed and parallel systems. All our protocols are simple, elegant and are based on performing disjoint transpositions executed in parallel. The challenging problem of our concern is to prove that ..."
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Cited by 19 (3 self)
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We analyze various stochastic processes for generating permutations almost uniformly at random in distributed and parallel systems. All our protocols are simple, elegant and are based on performing disjoint transpositions executed in parallel. The challenging problem of our concern is to prove that the output configurations in our processes reach almost uniform probability distribution very rapidly, i.e. in a (low) polylogarithmic time. For the analysis of the aforementioned protocols we develop a novel technique, called delayed path coupling, for proving rapid mixing of Markov chains. Our approach is an extension of the path coupling method of Bubley and Dyer. We apply delayed path coupling to three stochastic processes for generating random permutations. For one
Perfectly balanced allocation
 in Proceedings of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, Princeton, NJ, 2003, Lecture Notes in Comput. Sci. 2764
, 2003
"... Abstract. We investigate randomized processes underlying load balancing based on the multiplechoice paradigm: m balls have to be placed in n bins, and each ball can be placed into one out of 2 randomly selected bins. The aim is to distribute the balls as evenly as possible among the bins. Previousl ..."
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Cited by 18 (1 self)
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Abstract. We investigate randomized processes underlying load balancing based on the multiplechoice paradigm: m balls have to be placed in n bins, and each ball can be placed into one out of 2 randomly selected bins. The aim is to distribute the balls as evenly as possible among the bins. Previously, it was known that a simple process that places the balls one by one in the least loaded bin can achieve a maximum load of m/n + Θ(log log n) with high probability. Furthermore, it was known that it is possible to achieve (with high probability) a maximum load of at most ⌈m/n ⌉ +1using maximum flow computations. In this paper, we extend these results in several aspects. First of all, we show that if m ≥ cn log n for some sufficiently large c, thenaperfect distribution of balls among the bins can be achieved (i.e., the maximum load is ⌈m/n⌉) with high probability. The bound for m is essentially optimal, because it is known that if m ≤ c ′ n log n for some sufficiently small constant c ′ , the best possible maximum load that can be achieved is ⌈m/n ⌉ +1with high probability. Next, we analyze a simple, randomized load balancing process based on a local search paradigm. Our first result here is that this process always converges to a best possible load distribution. Then, we study the convergence speed of the process. We show that if m is sufficiently large compared to n,thenno matter with which ball distribution the system starts, if the imbalance is ∆, then the process needs only ∆·n O(1) steps to reach a perfect distribution, with high probability. We also prove a similar result for m ≈ n, and show that if m = O(n log n / log log n), then an optimal load distribution (which has the maximum load of ⌈m/n ⌉ +1) is reached by the random process after a polynomial number of steps, with high probability.