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118
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...
The Power of Two Random Choices: A Survey of Techniques and Results
 in Handbook of Randomized Computing
, 2000
"... 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 ..."
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Cited by 99 (2 self)
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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.,...
Tail Bounds for Occupancy and the Satisfiability Threshold Conjecture
, 1995
"... The classical occupancy problem is concerned with studying the number of empty bins resulting from a random allocation of m balls to n bins. We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and prob ..."
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Cited by 97 (1 self)
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The classical occupancy problem is concerned with studying the number of empty bins resulting from a random allocation of m balls to n bins. We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and probabilistic analysis. Our motivating application is the following wellknown conjecture on threshold phenomenon for the satisfiability problem. Consider random 3SAT formulas with cn clauses over n variables, where each clause is chosen uniformly and independently from the space of all clauses of size 3. It has been conjectured that there is a sharp threshold for satisfiability at c ß 4:2. We provide a strong upper bound on the value of c , showing that for c ? 4:758 a random 3SAT formula is unsatisfiable with high probability. This result is based on a structural property, possibly of independent interest, whose proof needs several applications of the occupancy tail bounds. Supporte...
A lineartime probabilistic counting algorithm for database applications
 ACM Transactions on Database Systems
, 1990
"... We present a probabilistic algorithm for counting the number of unique values in the presence of duplicates. This algorithm has O(q) time complexity, where q is the number of values including duplicates, and produces an estimation with an arbitrary accuracy prespecified by the user using only a smal ..."
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Cited by 92 (5 self)
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We present a probabilistic algorithm for counting the number of unique values in the presence of duplicates. This algorithm has O(q) time complexity, where q is the number of values including duplicates, and produces an estimation with an arbitrary accuracy prespecified by the user using only a small amount of space. Traditionally, accurate counts of unique values were obtained by sorting, which has O(q log q) time complexity. Our technique, called linear counting, is based on hashing. We present a comprehensive theoretical and experimental analysis of linear counting. The analysis reveals an interesting result: A load factor (number of unique values/hash table size) much larger than 1.0 (e.g., 12) can be used for accurate estimation (e.g., 1 % of error). We present this technique with two important applications to database problems: namely, (1) obtaining the column cardinality (the number of unique values in a column of a relation) and (2) obtaining the join selectivity (the number of unique values in the join column resulting from an unconditional join divided by the number of unique join column values in the relation to he joined). These two parameters are important statistics that are used in relational query optimization and physical database design.
Multiple Object Identification with Passive RFID Tags
, 2002
"... We investigate the applicability of passive RFID systems to the task of identifying multiple tagged objects simultaneously, assuming that the number of tags is not known in advance. We present a combinatorial model of the communication mechanism between the reader device and the tags, and use this m ..."
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Cited by 84 (0 self)
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We investigate the applicability of passive RFID systems to the task of identifying multiple tagged objects simultaneously, assuming that the number of tags is not known in advance. We present a combinatorial model of the communication mechanism between the reader device and the tags, and use this model to derive the optimal parameter setting for the reading process, based on estimates for the number of tags. Some results on the performance of an implementation are presented.
balls into bins” — A simple and tight analysis
 Lecture Notes in Computer Science
, 1998
"... Abstract. Suppose we sequentially throw m balls into n bins. It is a natural question to ask for the maximum number of balls in any bin. In this paper we shall derive sharp upper and lower bounds which are reached with high probability. We prove bounds for all values of m(n) n=polylog(n) by using th ..."
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Cited by 76 (2 self)
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Abstract. Suppose we sequentially throw m balls into n bins. It is a natural question to ask for the maximum number of balls in any bin. In this paper we shall derive sharp upper and lower bounds which are reached with high probability. We prove bounds for all values of m(n) n=polylog(n) by using the simple and wellknown method of the rst and second moment. 1
Statistical profile estimation in database systems
 ACM Comput. Surveys
, 1988
"... A statistical profile summarizes the instances of a database. It describes aspects such as the number of tuples, the number of values, the distribution of values, the correlation between value sets, and the distribution of tuples among secondary storage units. Estimation of database profiles is crit ..."
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Cited by 73 (0 self)
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A statistical profile summarizes the instances of a database. It describes aspects such as the number of tuples, the number of values, the distribution of values, the correlation between value sets, and the distribution of tuples among secondary storage units. Estimation of database profiles is critical in the problems of query optimization, physical database design, and database performance prediction. This paper describes a model of a database of profile, relates this model to estimating the cost of database operations, and surveys methods of estimating profiles. The operators and objects in the model include build profile, estimate profile, and update profile. The estimate operator is classified by the relational algebra operator (select, project, join), the property to be estimated (cardinality, distribution of values, and other parameters), and the underlying method (parametric, nonparametric, and adhoc). The accuracy, overhead, and assumptions of methods are discussed in detail. Relevant research in both the database and the statistics disciplines is incorporated in the detailed discussion.
Functional Limit Theorems For Multitype Branching Processes And Generalized Pólya Urns
 APPL
, 2004
"... A functional limit theorem is proved for multitype continuous time Markov branching processes. As consequences, we obtain limit theorems for the branching process stopped by some stopping rule, for example when the total number of particles reaches a given level. Using the ..."
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Cited by 67 (13 self)
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A functional limit theorem is proved for multitype continuous time Markov branching processes. As consequences, we obtain limit theorems for the branching process stopped by some stopping rule, for example when the total number of particles reaches a given level. Using the
Parallel Randomized Load Balancing
 In Symposium on Theory of Computing. ACM
, 1995
"... It is well known that after placing n balls independently and uniformly at random into n bins, the fullest bin holds \Theta(log n= log log n) balls with high probability. Recently, Azar et al. analyzed the following: randomly choose d bins for each ball, and then sequentially place each ball in the ..."
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Cited by 56 (8 self)
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It is well known that after placing n balls independently and uniformly at random into n bins, the fullest bin holds \Theta(log n= log log n) balls with high probability. Recently, Azar et al. analyzed the following: randomly choose d bins for each ball, and then sequentially place each ball in the least full of its chosen bins [2]. They show that the fullest bin contains only log log n= log d + \Theta(1) balls with high probability. We explore extensions of this result to parallel and distributed settings. Our results focus on the tradeoff between the amount of communication and the final load. Given r rounds of communication, we provide lower bounds on the maximum load of \Omega\Gamma r p log n= log log n) for a wide class of strategies. Our results extend to the case where the number of rounds is allowed to grow with n. We then demonstrate parallelizations of the sequential strategy presented in Azar et al. that achieve loads within a constant factor of the lower bound for two ...