Results 1  10
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408
Stable Distributions, Pseudorandom Generators, Embeddings and Data Stream Computation
, 2000
"... In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: ffl we show how to maintain (using only O(log n=ffl 2 ) words of storage) a sketch C(p) of a point p 2 l n 1 under dynamic updates of its coo ..."
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Cited by 324 (13 self)
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In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: ffl we show how to maintain (using only O(log n=ffl 2 ) words of storage) a sketch C(p) of a point p 2 l n 1 under dynamic updates of its
A SubConstant ErrorProbability LowDegree Test, and a SubConstant ErrorProbability PCP Characterization of NP
 IN PROC. 29TH ACM SYMP. ON THEORY OF COMPUTING, 475484. EL PASO
, 1997
"... We introduce a new lowdegreetest, one that uses the restriction of lowdegree polynomials to planes (i.e., affine subspaces of dimension 2), rather than the restriction to lines (i.e., affine subspaces of dimension 1). We prove the new test to be of a very small errorprobability (in particular, ..."
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Cited by 324 (20 self)
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, and such that the errorprobability is 2 \Gamma log 1\Gammaffl n . Our results are in fact stronger, as stated below. One application of the new characterization of NP is that approximating SETCOVER to within a logarithmic factors is NPhard. Previous analysis for lowdegreetests, as well as previous
The Final Measurement of Ffl
"... INTRODUCTION 1.1. CP violation in the neutral kaon system CP violation has been discovered in the neutral kaon system in 1964 [1]. The main component of the effect [2] occurs in the mixing between K 0 and K 0 . The physical states KS and KL deviate from pure CP = \Sigma 1 eigenstates, with the mi ..."
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= 1 \Gamma 6 \Theta Re(ffl In the Standard Model, CP violation arises from the irreducible complex phase in the CKM matrix [4]. Direct CP violation is predicted by the Standard Model, with typical computations for Re(ffl =ffl) ranging from 10 to 30 \Theta10 [5]. From the data taken in 1997
Maintaining Stream Statistics over Sliding Windows (Extended Abstract)
, 2002
"... We consider the problem of maintaining aggregates and statistics over data streams, with respect to the last N data elements seen so far. We refer to this model as the sliding window model. We consider the following basic problem: Given a stream of bits, maintain a count of the number of 1's i ..."
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Cited by 269 (9 self)
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;s in the last N elements seen from the stream. We show that using O( 1 ffl log 2 N) bits of memory, we can estimate the number of 1's to within a factor of 1 + ffl. We also give a matching lower bound of \Omega\Gamma 1 ffl log 2 N) memory bits for any deterministic or randomized algorithms. We
ffl)Approximation Scheme for the Euclidean TSP
, 1996
"... if the bounding box was the smallest possible, the length OPT of the optimum tour is at least 2n 2 (since there must be cities on the 2 shortest sides). Now, consider the instance obtained by rounding the coordinates of every city to the nearest integer. In the rounded instance, the distance betwe ..."
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location of any city (or vice versa), we derive that jl(T ) \Gamma l 0 (T )j p 2n: (1) Thus, if we have a (1 + ffl<
Learning Linear Threshold Functions in the Presence of Classification Noise
 In Proceedings of the Seventh Annual Workshop on Computational Learning Theory
, 1994
"... I show that linear threshold functions are polynomially learnable in the presence of classification noise, i.e., polynomial in n, 1=ffl, 1=ffi, and 1=oe, where n is the number of Boolean attributes, ffl and ffi are the usual accuracy and confidence parameters, and oe indicates the minimum dist ..."
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Cited by 35 (3 self)
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vector is added to the current weight vector. Similar modifications are shown for the Weighted Majority algorithm. The correction vector is simply the mean of the normalized examples. In the special case of Boolean threshold functions, the modified Perceptron algorithm performs O(n 2 ffl \Gamma
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
, 1999
"... We describe fully polynomial time approximation schemes for various multicommodity flow problems in graphs with m edges and n vertices. We present the first approximation scheme for maximum multicommodity flow that is independent of the number of commodities k, and our algorithm improves upon the ru ..."
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Cited by 110 (8 self)
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the runtime of previous algorithms by this factor of k, performing in O (ffl \Gamma2 m 2 ) time. For maximum concurrent flow, and minimum cost concurrent flow, we present algorithms that are faster than the current known algorithms when the graph is sparse or the number of commodities k is large, i
Adding Multiple Cost Constraints to Combinatorial Optimization Problems, with Applications to Multicommodity Flows
 IN PROCEEDINGS OF THE 27TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1995
"... Minimum cost multicommodity flow is an instance of a simpler problem (multicommodity flow) to which a cost constraint has been added. In this paper we present a general scheme for solving a large class of such "costadded" problemseven if more than one cost is added. One of the main ..."
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Cited by 45 (5 self)
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is the number vertices in the input problem. This improves the previous best deterministic bounds of O(ffl \Gamma4 kmn 2 ) [9] and ~ O(ffl \Gamma2 k 2 m 2 ) [15] by factors of n=ffl and fflkm=n respectively. In fact, it even dominates the best randomized bound of ~ O(ffl \Gamma2 km 2 ) [15
Approximation Algorithms for Directed Steiner Problems
 Journal of Algorithms
, 1998
"... We give the first nontrivial approximation algorithms for the Steiner tree problem and the generalized Steiner network problem on general directed graphs. These problems have several applications in network design and multicast routing. For both problems, the best ratios known before our work we ..."
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Cited by 178 (8 self)
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were the trivial O(k)approximations. For the directed Steiner tree problem, we design a family of algorithms that achieves an approximation ratio of i(i \Gamma 1)k 1=i in time O(n i k 2i ) for any fixed i ? 1, where k is the number of terminals. Thus, an O(k ffl ) approximation ratio can
Simple and Fast Distributed Multicommodity Flow Algorithm
"... In this paper, we present a simple and fast distributed algorithm for approximately solving the minimumcost multicommodity flow problem. If there exists a flow that satisfies all of the demands, our algorithm runs in O(m 2 ffl \Gamma2 log n) communication rounds and produces a flow that satisfi ..."
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Cited by 3 (1 self)
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In this paper, we present a simple and fast distributed algorithm for approximately solving the minimumcost multicommodity flow problem. If there exists a flow that satisfies all of the demands, our algorithm runs in O(m 2 ffl \Gamma2 log n) communication rounds and produces a flow
Results 1  10
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408