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NearOptimal Sublinear Time Bounds for Distributed Random Walks
, 2009
"... We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. Despite the widespread use of random walks in distributed computing theory and practice for long ..."
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to improve beyond linear time (in ℓ) despite the sequential nature of random walks. This work further conjectured that a running time of Õ( √ ℓD) is possible and that this is essentially optimal. In this paper, we resolve these conjectures and show almost tight bounds on the time complexity of distributed
NearOptimal Sublinear Time Algorithms for Ulam Distance
"... We give neartight bounds for estimating the edit distance between two nonrepetitive strings (Ulam distance) with constant approximation, in sublinear time. For two strings of length d and at edit distance R, our algorithm runs in time Õ(d/R + √ d) and outputs a constant approximation to R. We als ..."
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We give neartight bounds for estimating the edit distance between two nonrepetitive strings (Ulam distance) with constant approximation, in sublinear time. For two strings of length d and at edit distance R, our algorithm runs in time Õ(d/R + √ d) and outputs a constant approximation to R. We
NearOptimal Sublinear Time Algorithms for Ulam Distance
"... We give neartight bounds for estimating the edit distance between two nonrepetitive strings (Ulam distance) with constant approximation, in sublinear time. For two strings of length d and at edit distance R, our algorithm runs in time Õ(d/R + √ d) and outputs a constant approximation to R. We als ..."
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We give neartight bounds for estimating the edit distance between two nonrepetitive strings (Ulam distance) with constant approximation, in sublinear time. For two strings of length d and at edit distance R, our algorithm runs in time Õ(d/R + √ d) and outputs a constant approximation to R. We
NearOptimal Sublinear Time Algorithms for Ulam Distance
"... We give neartight bounds for estimating the edit distance between two nonrepetitive strings (Ulam distance) with constant approximation, in sublinear time. For two strings of length d and at edit distance R, our algorithm runs in time Õ(d/R + √ d) and outputs a constant approximation to R. We als ..."
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We give neartight bounds for estimating the edit distance between two nonrepetitive strings (Ulam distance) with constant approximation, in sublinear time. For two strings of length d and at edit distance R, our algorithm runs in time Õ(d/R + √ d) and outputs a constant approximation to R. We
Barriers to nearoptimal equilibria
 In Proceedings of the 55th Annual IEEE Symposium on Foundations of Computer Science (FOCS
"... Abstract—This paper explains when and how communication and computational lower bounds for algorithms for an optimization problem translate to lower bounds on the worstcase quality of equilibria in games derived from the problem. We give three families of lower bounds on the quality of equilibria, ..."
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the design of simple combinatorial auctions to the existence of effective tolls for routing networks — where the goal is to design a game that has only nearoptimal equilibria. For example, our results imply that the simultaneous firstprice auction format is optimal among all “simple combinatorial auctions
Improved Time Bounds for NearOptimal Sparse Fourier Representations
"... We study the problem of finding a Fourier representation R of m terms for a given discrete signal A of length N. The Fast Fourier Transform (FFT) can find the optimal Nterm representation in time O(N log N) time, but our goal is to get sublinear time algorithms when m ≪ N. ..."
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We study the problem of finding a Fourier representation R of m terms for a given discrete signal A of length N. The Fast Fourier Transform (FFT) can find the optimal Nterm representation in time O(N log N) time, but our goal is to get sublinear time algorithms when m ≪ N.
Coloring in Sublinear Time
 Proceedings of the ESA 1997, Springer Lecture Notes in Computer Science 1284
, 1997
"... We will present an algorithm, based on SAtechniques ... ..."
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Cited by 3 (1 self)
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We will present an algorithm, based on SAtechniques ...
Improved Time Bounds for NearOptimal Sparse Fourier Representations
 in Proc. SPIE Wavelets XI
, 2003
"... We study the problem of finding a Fourier representation R of B terms for a given discrete signal A of length N . The Fast Fourier Transform (FFT) can find the optimal Nterm representation in O(N log N) time, but our goal is to get sublinear algorithms for B ! N , typically, B N . Suppose kAk2 M ..."
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Cited by 58 (11 self)
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We study the problem of finding a Fourier representation R of B terms for a given discrete signal A of length N . The Fast Fourier Transform (FFT) can find the optimal Nterm representation in O(N log N) time, but our goal is to get sublinear algorithms for B ! N , typically, B N . Suppose kAk2
A NearOptimal SublinearTime Algorithm for Approximating the Minimum Vertex Cover Size
, 2011
"... We give a nearly optimal sublineartime algorithm for approximating the size of a minimum vertex cover in a graph G. The algorithm may query the degree deg(v) of any vertex v of its choice, and for each 1 ≤ i ≤ deg(v), it may ask for the ith neighbor of v. Letting VCopt(G) denote the minimum size of ..."
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Cited by 2 (1 self)
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We give a nearly optimal sublineartime algorithm for approximating the size of a minimum vertex cover in a graph G. The algorithm may query the degree deg(v) of any vertex v of its choice, and for each 1 ≤ i ≤ deg(v), it may ask for the ith neighbor of v. Letting VCopt(G) denote the minimum size
Nearoptimal sparse Fourier representations via sampling
 In STOC
, 2002
"... We give an algorithm for nding a Fourier representation R ofBterms for a given discrete signal A of lengthN, such thatkA,Rk 2 2 is within the factor (1 +) of best possible kA,Roptk 2 2. Our algorithm can access A by reading its values on a sample setT [0;N), chosen randomly from a (nonproduct) dist ..."
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Cited by 95 (24 self)
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product) distribution of our choice, independent of A. That is, we sample nonadaptively. The total time cost of the algorithm is polynomial inB log(N) log(M) = (where M is the ratio of largest to smallest numerical quantity encountered), which implies a similar bound for the number of samples. 1.
Results 1  10
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