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118,246
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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o(1)) ln n), and previous results of Lund and Yannakakis, that showed hardness of approximation within a ratio of (log 2 n)=2 ' 0:72 lnn. For max kcover we show an approximation threshold of (1 \Gamma 1=e) (up to low order terms), under the assumption that P != NP .
Worstcase equilibria
 IN PROCEEDINGS OF THE 16TH ANNUAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE
, 1999
"... In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a ver ..."
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Cited by 851 (17 self)
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In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.
How Much Training is Needed in MultipleAntenna Wireless Links?
 IEEE Trans. Inform. Theory
, 2000
"... .... ..."
Improved algorithms for optimal winner determination in combinatorial auctions and generalizations
, 2000
"... Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary. Determining the winners is NPcomplete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper present ..."
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Cited by 598 (55 self)
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Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary. Determining the winners is NPcomplete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper presents a more sophisticated search algorithm for optimal (and anytime) winner determination, including structural improvements that reduce search tree size, faster data structures, and optimizations at search nodes based on driving toward, identifying and solving tractable special cases. We also uncover a more general tractable special case, and design algorithms for solving it as well as for solving known tractable special cases substantially faster. We generalize combinatorial auctions to multiple units of each item, to reserve prices on singletons as well as combinations, and to combinatorial exchanges  all allowing for substitutability. Finally, we present algorithms for determining the winners in these generalizations.
Lag length selection and the construction of unit root tests with good size and power
 Econometrica
, 2001
"... It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We conside ..."
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Cited by 534 (14 self)
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It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We consider a class of Modified Information Criteria (MIC) with a penalty factor that is sample dependent. It takes into account the fact that the bias in the sum of the autoregressive coefficients is highly dependent on k and adapts to the type of deterministic components present. We use a local asymptotic framework in which the movingaverage root is local to −1 to document how the MIC performs better in selecting appropriate values of k. In montecarlo experiments, the MIC is found to yield huge size improvements to the DF GLS and the feasible point optimal PT test developed in Elliott, Rothenberg and Stock (1996). We also extend the M tests developed in Perron and Ng (1996) to allow for GLS detrending of the data. The MIC along with GLS detrended data yield a set of tests with desirable size and power properties.
Bigtable: A distributed storage system for structured data
 IN PROCEEDINGS OF THE 7TH CONFERENCE ON USENIX SYMPOSIUM ON OPERATING SYSTEMS DESIGN AND IMPLEMENTATION  VOLUME 7
, 2006
"... Bigtable is a distributed storage system for managing structured data that is designed to scale to a very large size: petabytes of data across thousands of commodity servers. Many projects at Google store data in Bigtable, including web indexing, Google Earth, and Google Finance. These applications ..."
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Cited by 995 (3 self)
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Bigtable is a distributed storage system for managing structured data that is designed to scale to a very large size: petabytes of data across thousands of commodity servers. Many projects at Google store data in Bigtable, including web indexing, Google Earth, and Google Finance. These applications place very different demands on Bigtable, both in terms of data size (from URLs to web pages to satellite imagery) and latency requirements (from backend bulk processing to realtime data serving). Despite these varied demands, Bigtable has successfully provided a flexible, highperformance solution for all of these Google products. In this paper we describe the simple data model provided by Bigtable, which gives clients dynamic control over data layout and format, and we describe the design and implementation of Bigtable.
A scheduling model for reduced CPU energy
 ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 1995
"... The energy usage of computer systems is becoming an important consideration, especially for batteryoperated systems. Various methods for reducing energy consumption have been investigated, both at the circuit level and at the operating systems level. In this paper, we propose a simple model of job s ..."
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Cited by 550 (3 self)
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The energy usage of computer systems is becoming an important consideration, especially for batteryoperated systems. Various methods for reducing energy consumption have been investigated, both at the circuit level and at the operating systems level. In this paper, we propose a simple model of job scheduling aimed at capturing some key aspects of energy minimization. In this model, each job is to be executed between its arrival time and deadline by a single processor with variable speed, under the assumption that energy usage per unit time, P, is a convex function of the processor speed s. We give an offline algorithm that computes, for any set of jobs, a minimumenergy schedule. We then consider some online algorithms and their competitive performance for the power function P(s) = sp where p 3 2. It is shown that one natural heuristic, called the Average Rate heuristic, uses at most a constant times the minimum energy required. The analysis involves bounding the largest eigenvalue in matrices of a special type.
NewsWeeder: Learning to Filter Netnews
 in Proceedings of the 12th International Machine Learning Conference (ML95
, 1995
"... A significant problem in many information filtering systems is the dependence on the user for the creation and maintenance of a user profile, which describes the user's interests. NewsWeeder is a netnewsfiltering system that addresses this problem by letting the user rate his or her interest l ..."
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Cited by 555 (0 self)
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A significant problem in many information filtering systems is the dependence on the user for the creation and maintenance of a user profile, which describes the user's interests. NewsWeeder is a netnewsfiltering system that addresses this problem by letting the user rate his or her interest level for each article being read (15), and then learning a user profile based on these ratings. This paper describes how NewsWeeder accomplishes this task, and examines the alternative learning methods used. The results show that a learning algorithm based on the Minimum Description Length (MDL) principle was able to raise the percentage of interesting articles to be shown to users from 14% to 52% on average. Further, this performance significantly outperformed (by 21%) one of the most successful techniques in Information Retrieval (IR), termfrequency /inversedocumentfrequency (tfidf) weighting. 1
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