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176
How to Use Expert Advice
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1997
"... We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worstcase situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the ..."
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Cited by 377 (79 self)
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We analyze algorithms that predict a binary value by combining the predictions of several prediction strategies, called experts. Our analysis is for worstcase situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the algorithm by the difference between the expected number of mistakes it makes on the bit sequence and the expected number of mistakes made by the best expert on this sequence, where the expectation is taken with respect to the randomization in the predictions. We show that the minimum achievable difference is on the order of the square root of the number of mistakes of the best expert, and we give efficient algorithms that achieve this. Our upper and lower bounds have matching leading constants in most cases. We then show howthis leads to certain kinds of pattern recognition/learning algorithms with performance bounds that improve on the best results currently known in this context. We also compare our analysis to the case in which log loss is used instead of the expected number of mistakes.
Probabilistic Approximation of Metric Spaces and its Algorithmic Applications
 In 37th Annual Symposium on Foundations of Computer Science
, 1996
"... The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized ..."
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Cited by 351 (32 self)
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The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized algorithms for optimization problems on metric spaces, by relating the randomized performance ratio for any metric space to the randomized performance ratio for a set of "simple" metric spaces. We define a notion of a set of metric spaces that probabilisticallyapproximates another metric space. We prove that any metric space can be probabilisticallyapproximated by hierarchically wellseparated trees (HST) with a polylogarithmic distortion. These metric spaces are "simple" as being: (1) tree metrics. (2) natural for applying a divideandconquer algorithmic approach. The technique presented is of particular interest in the context of online computation. A large number of online al...
Optimal Prefetching via Data Compression
, 1995
"... Caching and prefetching are important mechanisms for speeding up access time to data on secondary storage. Recent work in competitive online algorithms has uncovered several promising new algorithms for caching. In this paper we apply a form of the competitive philosophy for the first time to the pr ..."
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Cited by 258 (7 self)
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Caching and prefetching are important mechanisms for speeding up access time to data on secondary storage. Recent work in competitive online algorithms has uncovered several promising new algorithms for caching. In this paper we apply a form of the competitive philosophy for the first time to the problem of prefetching to develop an optimal universal prefetcher in terms of fault ratio, with particular applications to largescale databases and hypertext systems. Our prediction algorithms for prefetching are novel in that they are based on data compression techniques that are both theoretically optimal and good in practice. Intuitively, in order to compress data effectively, you have to be able to predict future data well, and thus good data compressors should be able to predict well for purposes of prefetching. We show for powerful models such as Markov sources and nth order Markov sources that the page fault rates incurred by our prefetching algorithms are optimal in the limit for almost all sequences of page requests.
An optimal online algorithm for metrical task systems
 JOURNAL OF THE ACM
, 1992
"... 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 decision algorithm is developed. It is shown that, for an importan ..."
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Cited by 209 (8 self)
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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 decision 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 sequence 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) =
A GraphTheoretic Game and its Application to the kServer Problem
 SIAM J. COMPUT
, 1995
"... This paper investigates a zerosum game played on a weighted connected graph G between two players, the tree player and the edge player. At each play, the tree player chooses a spanning tree T and the edge player chooses an edge e. The payoff to the edge player is cost(T; e), defined as follows: If ..."
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Cited by 139 (4 self)
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This paper investigates a zerosum game played on a weighted connected graph G between two players, the tree player and the edge player. At each play, the tree player chooses a spanning tree T and the edge player chooses an edge e. The payoff to the edge player is cost(T; e), defined as follows: If e lies in the tree T then cost(T; e) = 0; if e does not lie in the tree then cost(T; e) = cycle(T; e)=w(e), where w(e) is the weight of edge e and cycle(T; e) is the weight of the unique cycle formed when edge e is added to the tree T. Our main result is that the value of the game on any nvertex graph is bounded above by exp(O( p log n log log n)). The game arises in connection with the kserver problem on a road network; i.e., a metric space that can be represented as a multigraph G in which each edge e represents a road of length w(e). We show that, if the value of the game on G is V al(G; w), then there is a randomized strategy that achieves a competitive ratio of k(1 + V al(G; w)) against any oblivious adversary. Thus, on any nvertex road network, there is a randomized algorithm for the kserver problem that is k exp(O( p log n log log n))competitive against oblivious adversaries. At the heart of our analysis of the game is an algorithm that, for any nvertex weighted, connected multigraph, constructs a spanning tree T such
BEYOND COMPETITIVE ANALYSIS
, 2000
"... The competitive analysis of online algorithms has been criticized as being too crude and unrealistic. We propose refinements of competitive analysis in two directions: The first restricts the power of the adversary by allowingonly certain input distributions, while the other allows for comparisons ..."
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Cited by 132 (3 self)
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The competitive analysis of online algorithms has been criticized as being too crude and unrealistic. We propose refinements of competitive analysis in two directions: The first restricts the power of the adversary by allowingonly certain input distributions, while the other allows for comparisons between information regimes for online decisionmaking. We illustrate the first with an application to the paging problem; as a byproduct we characterize completely the work functions of this important special case of the kserver problem. We use the second refinement to explore the power of lookahead in server and task systems.
The Competitiveness of OnLine Assignments
, 1992
"... Consider the online problem where a number of servers are ready to provide service to a set of customers. Each customer's job can be handled by any of a subset of the servers. Customers arrive onebyone and the problem is to assign each customer to an appropriate server in a manner that will ..."
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Cited by 110 (19 self)
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Consider the online problem where a number of servers are ready to provide service to a set of customers. Each customer's job can be handled by any of a subset of the servers. Customers arrive onebyone and the problem is to assign each customer to an appropriate server in a manner that will balance the load on the servers. This problem can be modeled in a natural way by a bipartite graph where the vertices of one side (customers) appear one at a time and the vertices of the other side (servers) are known in advance. We derive tight bounds on the competitive ratio in both deterministic and randomized cases. Let n denote the number of servers. In the deterministic case we provide an online algorithm that achieves a competitive ratio of k = dlog 2 ne (up to an additive 1) and prove that this is the best competitive ratio that can be achieved by any deterministic online algorithm. In a similar way we prove that the competitive ratio for the randomized case is k 0 = ln(n) (up to an a...
Competitive NonPreemptive Call Control
"... We deal with randomized competitive algorithms for nonpreemptive call control on treelike switching networks. We give an optimal O(log n) competitive algorithm for nonpreemptive call scheduling on trees. We then extend the problem to include variable call rates, call durations, and arbitrary call ..."
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Cited by 105 (8 self)
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We deal with randomized competitive algorithms for nonpreemptive call control on treelike switching networks. We give an optimal O(log n) competitive algorithm for nonpreemptive call scheduling on trees. We then extend the problem to include variable call rates, call durations, and arbitrary call benefits, and obtain a polylog competitive algorithm. We also show that many similar algorithms for different problems that can deal with constant values of parameters such as rates and benefits can be transformed into randomized algorithms that can deal with varying values of the parameters.
Competitive Algorithms for Distributed Data Management
 In Proceedings of the 24th Annual ACM Symposium on Theory of Computing
"... We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so ..."
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Cited by 101 (8 self)
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We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so as to optimize communication costs, but multiple copies must be kept consistent and at least one copy must be stored somewhere in the network at all times. We deal with competitive algorithms for minimizing communication costs, over arbitrary sequences of reads and writes, and arbitrary network topologies. We define the constrained file allocation problem to be the solution of many individual file allocation problems simultaneously, subject to the constraints of local memory size. We give competitive algorithms for this problem on the uniform network topology. We then introduce distributed competitive algorithms for online data tracking (a generalization of mobile user tracking [AP1...