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676
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 555 (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
Competitive auctions and digital goods
 In Proc. 12th Symp. on Discrete Alg
, 2001
"... Abstract We study a class of single round, sealed bid auctions for items in unlimited supply such as digital goods. We focus on auctions that are truthful and competitive. Truthful auctions encourage bidders to bid their utility; competitive auctions yield revenue within a constant factor of the rev ..."
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Cited by 126 (26 self)
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Abstract We study a class of single round, sealed bid auctions for items in unlimited supply such as digital goods. We focus on auctions that are truthful and competitive. Truthful auctions encourage bidders to bid their utility; competitive auctions yield revenue within a constant factor of the revenue for optimal fixed pricing. We show that for any truthful auction, even a multiprice auction, the expected revenue does not exceed that for optimal fixed pricing. We also give a bound on how far the revenue for optimal fixed pricing can be from the total market utility. We show that several randomized auctions are truthful and competitive under certain assumptions, and that no truthful deterministic auction is competitive. We present simulation results which confirm that our auctions compare favorably to fixed pricing. Some of our results extend to bounded supply markets, for which we also get truthful and competitive auctions.
Online Routing in Triangulations
 IN PROC. OF THE 10 TH ANNUAL INT. SYMP. ON ALGORITHMS AND COMPUTATION ISAAC
, 1999
"... We consider online routing strategies for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing strategies, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a ..."
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Cited by 109 (12 self)
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We consider online routing strategies for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing strategies, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a randomized memoryless strategy that works for all triangulations, (3) an O(1) memory strategy that works for all convex subdivisions, (4) an O(1) memory strategy that approximates the shortest path in Delaunay triangulations, and (5) theoretical and experimental results on the competitiveness of these strategies.
Competitive analysis of incentive compatible online auctions
 Theoretical Computer Science
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Competitive Auctions
, 2002
"... We study a class of singleround, sealedbid auctions for items in unlimited supply, such as digital goods. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages buyers to bid their utility) and yields profit that is roughly within a constant factor of ..."
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Cited by 81 (10 self)
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We study a class of singleround, sealedbid auctions for items in unlimited supply, such as digital goods. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages buyers to bid their utility) and yields profit that is roughly within a constant factor of the profit of optimal fixed pricing for all inputs. We justify the use of optimal fixed pricing as a benchmark for evaluating competitive auction profit. We show that several randomized auctions are truthful and competitive and that no truthful deterministic auction is competitive. Our results extend to bounded supply markets, for which we also get truthful and competitive auctions.
CacheOblivious Algorithms
, 1999
"... This thesis presents "cacheoblivious" algorithms that use asymptotically optimal amounts of work, and move data asymptotically optimally among multiple levels of cache. An algorithm is cache oblivious if no program variables dependent on hardware configuration parameters, such as cache si ..."
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Cited by 80 (1 self)
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This thesis presents "cacheoblivious" algorithms that use asymptotically optimal amounts of work, and move data asymptotically optimally among multiple levels of cache. An algorithm is cache oblivious if no program variables dependent on hardware configuration parameters, such as cache size and cacheline length need to be tuned to minimize the number of cache misses. We show that the ordinary algorithms for matrix transposition, matrix multiplication, sorting, and Jacobistyle multipass filtering are not cache optimal. We present algorithms for rectangular matrix transposition, FFT, sorting, and multipass filters, which are asymptotically optimal on computers with multiple levels of caches. For a cache with size Z and cacheline length L, where Z =# (L 2 ), the number of cache misses for an m &times; n matrix transpose is #(1 + mn=L). The number of cache misses for either an npoint FFT or the sorting of n numbers is #(1 + (n=L)(1 + log Z n)). The cache complexity of computing n ...
The Online Median Problem
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... We introduce a natural variant of the (metric uncapacitated) kmedian problem that we call the online median problem. Whereas the kmedian problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the following additional constraints: the facilities ar ..."
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Cited by 74 (2 self)
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We introduce a natural variant of the (metric uncapacitated) kmedian problem that we call the online median problem. Whereas the kmedian problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the following additional constraints: the facilities are placed one at a time; a facility cannot be moved once it is placed, and the total number of facilities to be placed, k, is not known in advance. The objective of an online median algorithm is to minimize the competitive ratio, that is, the worstcase ratio of the cost of an online placement to that of an optimal offline placement. Our main result is a lineartime constantcompetitive algorithm for the online median problem. In addition, we present a related, though substantially simpler, lineartime constantfactor approximation algorithm for the (metric uncapacitated) facility location problem. The latter algorithm is similar in spirit to the recent primaldualbased facility location algorithm of Jain and Vazirani, but our approach is more elementary and yields an improved running time.
Hedging uncertainty: Approximation algorithms for stochastic optimization problems
 In Proceedings of the 10th International Conference on Integer Programming and Combinatorial Optimization
, 2004
"... We initiate the design of approximation algorithms for stochastic combinatorial optimization problems; we formulate the problems in the framework of twostage stochastic optimization, and provide nearly tight approximation algorithms. Our problems range from the simple (shortest path, vertex cover, ..."
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Cited by 67 (10 self)
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We initiate the design of approximation algorithms for stochastic combinatorial optimization problems; we formulate the problems in the framework of twostage stochastic optimization, and provide nearly tight approximation algorithms. Our problems range from the simple (shortest path, vertex cover, bin packing) to complex (facility location, set cover), and contain representatives with different approximation ratios. The approximation ratio of the stochastic variant of a typical problem is of the same order of magnitude as its deterministic counterpart. Furthermore, common techniques for designing approximation algorithms such as LP rounding, the primaldual method, and the greedy algorithm, can be carefully adapted to obtain these results. 1
EnergyEfficient Algorithms for . . .
, 2007
"... We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good respons ..."
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Cited by 65 (2 self)
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We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variablespeed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unitsize jobs. We devise a deterministic constant competitive online algorithm and show that
A secondorder perceptron algorithm
, 2005
"... Kernelbased linearthreshold algorithms, such as support vector machines and Perceptronlike algorithms, are among the best available techniques for solving pattern classification problems. In this paper, we describe an extension of the classical Perceptron algorithm, called secondorder Perceptr ..."
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Cited by 59 (20 self)
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Kernelbased linearthreshold algorithms, such as support vector machines and Perceptronlike algorithms, are among the best available techniques for solving pattern classification problems. In this paper, we describe an extension of the classical Perceptron algorithm, called secondorder Perceptron, and analyze its performance within the mistake bound model of online learning. The bound achieved by our algorithm depends on the sensitivity to secondorder data information and is the best known mistake bound for (efficient) kernelbased linearthreshold classifiers to date. This mistake bound, which strictly generalizes the wellknown Perceptron bound, is expressed in terms of the eigenvalues of the empirical data correlation matrix and depends on a parameter controlling the sensitivity of the algorithm to the distribution of these eigenvalues. Since the optimal setting of this parameter is not known a priori, we also analyze two variants of the secondorder Perceptron algorithm: one that adaptively sets the value of the parameter in terms of the number of mistakes made so far, and one that is parameterless, based on pseudoinverses.