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102
The Power of Two Choices in Randomized Load Balancing
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 1996
"... Suppose that n balls are placed into n bins, each ball being placed into a bin chosen independently and uniformly at random. Then, with high probability, the maximum load in any bin is approximately log n log log n . Suppose instead that each ball is placed sequentially into the least full of d ..."
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Cited by 201 (23 self)
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Suppose that n balls are placed into n bins, each ball being placed into a bin chosen independently and uniformly at random. Then, with high probability, the maximum load in any bin is approximately log n log log n . Suppose instead that each ball is placed sequentially into the least full of d bins chosen independently and uniformly at random. It has recently been shown that the maximum load is then only log log n log d +O(1) with high probability. Thus giving each ball two choices instead of just one leads to an exponential improvement in the maximum load. This result demonstrates the power of two choices, and it has several applications to load balancing in distributed systems. In this thesis, we expand upon this result by examining related models and by developing techniques for stu...
Performance Modeling of Epidemic Routing
 In Proceedings of IFIP Networking
, 2006
"... Abstract. In this paper, we develop a rigorous, unified framework based on Ordinary Differential Equations (ODEs) to study epidemic routing and its variations. These ODEs can be derived as limits of Markovian models under a natural scaling as the number of nodes increases. While an analytical study ..."
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Cited by 110 (9 self)
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Abstract. In this paper, we develop a rigorous, unified framework based on Ordinary Differential Equations (ODEs) to study epidemic routing and its variations. These ODEs can be derived as limits of Markovian models under a natural scaling as the number of nodes increases. While an analytical study of Markovian models is quite complex and numerical solution impractical for large networks, the corresponding ODE models yield closedform expressions for several performance metrics of interest, and a numerical solution complexity that does not increase with the number of nodes. Using this ODE approach, we investigate how resources such as buffer space and power can be traded for faster delivery, illustrating the differences among the various epidemic schemes considered. Finally we consider the effect of buffer management by complementing the forwarding models with Markovian and fluid buffer models.
Using Multiple Hash Functions to Improve IP Lookups
 IN PROCEEDINGS OF IEEE INFOCOM
, 2000
"... High performance Internet routers require a mechanism for very efficient IP address lookups. Some techniques used to this end, such as binary search on levels, need to construct quickly a good hash table for the appropriate IP prefixes. In this paper we describe an approach for obtaining good hash ..."
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Cited by 68 (11 self)
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High performance Internet routers require a mechanism for very efficient IP address lookups. Some techniques used to this end, such as binary search on levels, need to construct quickly a good hash table for the appropriate IP prefixes. In this paper we describe an approach for obtaining good hash tables based on using multiple hashes of each input key (which is an IP address). The methods we describe are fast, simple, scalable, parallelizable, and flexible. In particular, in instances where the goal is to have one hash bucket fit into a cache line, using multiple hashes proves extremely suitable. We provide a general analysis of this hashing technique and specifically discuss its application to binary search on levels.
Optimal myopic algorithms for random 3SAT
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... Let F 3 (n; m) be a random 3SAT formula formed by selecting uniformly, independently, and with replacement, m clauses among all 8 \Gamma n 3 \Delta possible 3clauses over n variables. It has been conjectured that there exists a constant r 3 such that for any ffl ? 0, F 3 (n; (r 3 \Gamma ffl)n ..."
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Cited by 67 (8 self)
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Let F 3 (n; m) be a random 3SAT formula formed by selecting uniformly, independently, and with replacement, m clauses among all 8 \Gamma n 3 \Delta possible 3clauses over n variables. It has been conjectured that there exists a constant r 3 such that for any ffl ? 0, F 3 (n; (r 3 \Gamma ffl)n) is almost surely satisfiable, but F 3 (n; (r 3 + ffl)n) is almost surely unsatisfiable. The best lower bounds for the potential value of r 3 have come from analyzing rather simple extensions of unitclause propagation. Recently, it was shown [2] that all these extensions can be cast in a common framework and analyzed in a uniform manner by employing differential equations. Here, we determine optimal algorithms expressible in that framework, establishing r 3 ? 3:26. We extend the analysis via differential equations, and make extensive use of a new optimization problem we call "maxdensity multiplechoice knapsack". The structure of optimal knapsack solutions elegantly characterizes the choi...
On the Analysis of Randomized Load Balancing Schemes
 IN PROCEEDINGS OF THE 9TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1998
"... It is well known that simple randomized load balancing schemes can balance load effectively while incurring only a small overhead, making such schemes appealing for practical systems. In this paper, we provide new analyses for several such dynamic randomized load balancing schemes. Our work extends ..."
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Cited by 55 (7 self)
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It is well known that simple randomized load balancing schemes can balance load effectively while incurring only a small overhead, making such schemes appealing for practical systems. In this paper, we provide new analyses for several such dynamic randomized load balancing schemes. Our work extends a previous analysis of the supermarket model, a model that abstracts a simple, efficient load balancing scheme in the setting where jobs arrive at a large system of parallel processors. In this model, customers arrive at a system of n servers as a Poisson stream of rate #n, # < 1, with service requirements exponentially distributed with mean 1. Each customer chooses d servers independently and uniformly at random from the n servers, and is served according to the First In First Out (FIFO) protocol at the choice with the fewest customers. For the supermarket model, it has been shown that using d = 2 choices yields an exponential improvement in the expected time a customer spends in the syst...
Maximum matchings in sparse random graphs: KarpSipser revisited
, 1997
"... We study the average performance of a simple greedy algorithm for finding a matching in a sparse random graph G n;c=n , where c ? 0 is constant. The algorithm was first proposed by Karp and Sipser [12]. We give significantly improved estimates of the errors made by the algorithm. For the subcritica ..."
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Cited by 35 (10 self)
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We study the average performance of a simple greedy algorithm for finding a matching in a sparse random graph G n;c=n , where c ? 0 is constant. The algorithm was first proposed by Karp and Sipser [12]. We give significantly improved estimates of the errors made by the algorithm. For the subcritical case where c ! e we show that the algorithm finds a maximum matching with high probability. If c ? e then with high probability the algorithm produces a matching which is within n 1=5+o(1) of maximum size. 1 Introduction A matching in a graph G = (V; E) is a set of edges in E which are vertex disjoint. A standard problem in algorithmic graph theory is to find the largest possible matching in a graph. The first polynomial time algorithm to solve this problem was devised by Edmonds in 1965 and runs in time O(jV j 4 ) [10]. Over the years, many improvements have been made. Currently the fastest such algorithm is that of Micali and Vazirani which dates back to 1980. Its running time is O(...
2001. Metastability in stochastic dynamics of disordered meanfield models, Probab. Theory Related Fields 119
"... Abstract: We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of t ..."
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Cited by 32 (10 self)
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Abstract: We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding Gibbs measures. We derive the analog of the WentzellFreidlin theory in this case, showing that any transition can be decomposed, with probability exponentially close to one, into a deterministic sequence of “admissible transitions”. For these admissible transitions we give upper and lower bounds on the expected transition times that differ only by a factor √ N, where N denotes the volume of the system. The distribution rescaled transition times are shown to converge to the exponential distribution. We exemplify our results in the context of the random field CurieWeiss model.
Mean FDE Models for Internet Congestion Control Under a ManyFlows Regime
 IEEE Transactions on Information Theory
, 2001
"... Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduc ..."
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Cited by 30 (11 self)
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Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduced in the packet arrival and service processes due to many factors such as arrivals and departures of sources and uncontrollable short flows in the network. To make the analysis or simulation tractable, often deterministic fluid approximations of these algorithms are used. These approximations are in the form of either deterministic delay differential equations, or more generally, deterministic functional differential equations (FDEs). In this paper, we ignore the complexity introduced by the windowbased implementation of such algorithms and focus on the randomness in the network. We justify the use of deterministic models for proportionallyfair congestion controllers under a limiting regime where the number of flows in a network is large.
A fluid analysis framework for a Markovian process algebra
, 2010
"... Markovian process algebras, such as PEPA and stochastic πcalculus, bring a powerful compositional approach to the performance modelling of complex systems. However, the models generated by process algebras, as with other interleaving formalisms, are susceptible to the state space explosion problem. ..."
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Cited by 28 (23 self)
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Markovian process algebras, such as PEPA and stochastic πcalculus, bring a powerful compositional approach to the performance modelling of complex systems. However, the models generated by process algebras, as with other interleaving formalisms, are susceptible to the state space explosion problem. Models with only a modest number of process algebra terms can easily generate so many states that they are all but intractable to traditional solution techniques. Previous work aimed at addressing this problem has presented a fluidflow approximation allowing the analysis of systems which would otherwise be inaccessible. To achieve this, systems of ordinary differential equations describing the fluid flow of the stochastic process algebra model are generated informally. In this paper, we show formally that for a large class of models, this fluidflow analysis can be directly derived from the stochastic process algebra model as an approximation to the mean number of component types within the model. The nature of the fluid approximation is derived and characterised by direct comparison with the Chapman–Kolmogorov equations underlying the Markov model. Furthermore, we compare the fluid approximation with the exact solution using stochastic simulation and we are able to demonstrate that it is a very accurate approximation in many cases. For the first time, we also show how to extend these techniques naturally to generate systems of differential equations approximating higher order moments of model component counts. These are important performance characteristics for estimating, for instance, the variance of the component counts. This is very necessary if we are to understand how precise the fluidflow calculation is, in a given modelling situation.
Studying Balanced Allocations with Differential Equations
 COMBINATORICS, PROBABILITY, AND COMPUTING
, 1997
"... Using differential equations, we examine the GREEDY algorithm studied by Azar, Broder, Karlin, and Upfal for distributed load balancing [1]. This approach yields accurate estimates of the actual load distribution, provides insight into the exponential improvement GREEDY offers over simple random sel ..."
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Cited by 21 (3 self)
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Using differential equations, we examine the GREEDY algorithm studied by Azar, Broder, Karlin, and Upfal for distributed load balancing [1]. This approach yields accurate estimates of the actual load distribution, provides insight into the exponential improvement GREEDY offers over simple random selection, and allows one to prove tight concentration theorems about the loads in a straightforward manner.