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411
Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
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Cited by 2229 (37 self)
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Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simplest, or both. A randomized algorithm is an algorithm that uses random numbers to influence the choices it makes in the course of its computation. Thus its behavior (typically quantified as running time or quality of output) varies from
Optimal Aggregation Algorithms for Middleware
 IN PODS
, 2001
"... Assume that each object in a database has m grades, or scores, one for each of m attributes. For example, an object can have a color grade, that tells how red it is, and a shape grade, that tells how round it is. For each attribute, there is a sorted list, which lists each object and its grade under ..."
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Cited by 702 (4 self)
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Assume that each object in a database has m grades, or scores, one for each of m attributes. For example, an object can have a color grade, that tells how red it is, and a shape grade, that tells how round it is. For each attribute, there is a sorted list, which lists each object and its grade under that attribute, sorted by grade (highest grade first). There is some monotone aggregation function, or combining rule, such as min or average, that combines the individual grades to obtain an overall grade. To determine the top k objects (that have the best overall grades), the naive algorithm must access every object in the database, to find its grade under each attribute. Fagin has given an algorithm (“Fagin’s Algorithm”, or FA) that is much more efficient. For some monotone aggregation functions, FA is optimal with high probability in the worst case. We analyze an elegant and remarkably simple algorithm (“the threshold algorithm”, or TA) that is optimal in a much stronger sense than FA. We show that TA is essentially optimal, not just for some monotone aggregation functions, but for all of them, and not just in a highprobability worstcase sense, but over every database. Unlike FA, which requires large buffers (whose size may grow unboundedly as the database size grows), TA requires only a small, constantsize buffer. TA allows early stopping, which yields, in a precise sense, an approximate version of the top k answers. We distinguish
Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity
, 1988
"... , Introduction and References only) Benny Chor Oded Goldreich MIT \Gamma Laboratory for Computer Science Cambridge, Massachusetts 02139 ABSTRACT \Gamma A new model for weak random physical sources is presented. The new model strictly generalizes previous models (e.g. the Santha and Vazirani model [2 ..."
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Cited by 219 (6 self)
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, Introduction and References only) Benny Chor Oded Goldreich MIT \Gamma Laboratory for Computer Science Cambridge, Massachusetts 02139 ABSTRACT \Gamma A new model for weak random physical sources is presented. The new model strictly generalizes previous models (e.g. the Santha and Vazirani model [24]). The sources considered output strings according to probability distributions in which no single string is too probable. The new model provides a fruitful viewpoint on problems studied previously as: ffl Extracting almost perfect bits from sources of weak randomness: the question of possibility as well as the question of efficiency of such extraction schemes are addressed. ffl Probabilistic Communication Complexity: it is shown that most functions have linear communication complexity in a very strong probabilistic sense. ffl Robustness of BPP with respect to sources of weak randomness (generalizing a result of Vazirani and Vazirani [27]). The paper has appeared in SIAM Journal o...
An optimal online algorithm for metrical task systems
 Journal of the ACM
, 1992
"... Abstract. In practice, almost all dynamic systems require decisions to be made online, without full knowledge of their future impact on the system. A general model for the processing of sequences of tasks is introduced, and a general online decnion algorithm is developed. It is shown that, for an ..."
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Cited by 213 (8 self)
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Abstract. In practice, almost all dynamic systems require decisions to be made online, without full knowledge of their future impact on the system. A general model for the processing of sequences of tasks is introduced, and a general online decnion algorithm is developed. It is shown that, for an important algorithms. class of special cases, this algorithm is optimal among all online Specifically, a task system (S. d) for processing sequences of tasks consists of a set S of states and a cost matrix d where d(i, j) is the cost of changing from state i to state j (we assume that d satisfies the triangle inequality and all diagonal entries are f)). The cost of processing a given task depends on the state of the system. A schedule for a sequence T1, T2,..., Tk of tasks is a ‘equence sl,s~,..., Sk of states where s ~ is the state in which T ’ is processed; the cost of a schedule is the sum of all task processing costs and state transition costs incurred. An online scheduling algorithm is one that chooses s, only knowing T1 Tz ~.. T’. Such an algorithm is wcompetitive if, on any input task sequence, its cost is within an additive constant of w times the optimal offline schedule cost. The competitive ratio w(S, d) is the infimum w for which there is a wcompetitive online scheduling algorithm for (S, d). It is shown that w(S, d) = 2 ISI – 1 for eoery task system in which d is symmetric, and w(S, d) = 0(1 S]2) for every task system. Finally, randomized online scheduling algorithms are introduced. It is shown that for the uniform task system (in which d(i, j) = 1 for all i, j), the expected competitive ratio w(S, d) =
Adwords and generalized online matching
 In FOCS ’05: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
, 2005
"... How does a search engine company decide what ads to display with each query so as to maximize its revenue? This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a tradeoff revealing LP and use it to derive two optimal algorithms achieving competit ..."
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Cited by 148 (6 self)
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How does a search engine company decide what ads to display with each query so as to maximize its revenue? This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a tradeoff revealing LP and use it to derive two optimal algorithms achieving competitive ratios of 1 − 1/e for this problem. 1
Settling the complexity of twoplayer Nash equilibrium
 in: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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Competitive Paging With Locality of Reference
 Journal of Computer and System Sciences
, 1991
"... Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations ..."
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Cited by 128 (3 self)
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Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations about the model, citing its inability to discern between LRU and FIFO (algorithms whose performances differ markedly in practice), and the fact that the theoretical competitiveness of LRU is much larger than observed in practice. In addition, we would like to address the following important question: given some knowledge of a program's reference pattern, can we use it to improve paging performance on that program?
Fast Algorithms for Finding Randomized Strategies in Game Trees
, 1994
"... Interactions among agents can be conveniently described by game trees. In order to analyze a game, it is important to derive optimal (or equilibrium) strategies for the different players. The standard approach to finding such strategies in games with imperfect information is, in general, computation ..."
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Cited by 119 (11 self)
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Interactions among agents can be conveniently described by game trees. In order to analyze a game, it is important to derive optimal (or equilibrium) strategies for the different players. The standard approach to finding such strategies in games with imperfect information is, in general, computationally intractable. The approach is to generate the normal form of the game (the matrix containing the payoff for each strategy combination), and then solve a linear program (LP) or a linear complementarity problem (LCP). The size of the normal form, however, is typically exponential in the size of the game tree, thus making this method impractical in all but the simplest cases. This paper describes a new representation of strategies which results in a practical linear formulation of the problem of twoplayer games with perfect recall (i.e., games where players never forget anything, which is a standard assumption). Standard LP or LCP solvers can then be applied to find optimal randomized strategies. The resulting algorithms are, in general, exponentially better than the standard ones, both in terms of time and in terms of space.
Labeling Dynamic XML Trees
, 2002
"... We present algorithms to label the nodes of an XML tree which is subject to insertions and deletions of nodes. The labeling is done such that (1) we label each node immediately when it is inserted and this label remains unchanged, and (2) from a pair of labels alone, we can decide whether one node ..."
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Cited by 119 (3 self)
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We present algorithms to label the nodes of an XML tree which is subject to insertions and deletions of nodes. The labeling is done such that (1) we label each node immediately when it is inserted and this label remains unchanged, and (2) from a pair of labels alone, we can decide whether one node is an ancestor of the other. This problem arises in the context of XML databases that support queries on the structure of the documents as well as on the changes made to the documents over time. We prove that our algorithms assign the shortest possible labels (up to a constant factor) which satisfy these requirements. We also consider the same problem when &quot;clues &quot; that provide guarantees on possible future insertions are given together with newly inserted nodes. Such clues can be derived from the DTD or from statistics on similar XML trees. We present algorithms that use the clues to assign shorter labels. We also prove that the length of our labels is close to the minimum possible.