Improving the performance guarantee for approximate graph coloring
Journal of the ACM (JACM)
The Johnson-Lindenstrauss Lemma and the sphericity of some graphs
Journal of Combinatorial Theory Series A
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Latent semantic indexing: a probabilistic analysis
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Subquadratic approximation algorithms for clustering problems in high dimensional spaces
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Reductions among high dimensional proximity problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A new way of using semidefinite programming with applications to linear equations mod p
Journal of Algorithms
Database-friendly random projections
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Identifying Representative Trends in Massive Time Series Data Sets Using Sketches
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Learning Mixtures of Gaussians
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Similarity estimation techniques from rounding algorithms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithmic derandomization via complexity theory
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Reductions in streaming algorithms, with an application to counting triangles in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
An elementary proof of a theorem of Johnson and Lindenstrauss
Random Structures & Algorithms
Experiments with random projections for machine learning
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Journal of the ACM (JACM)
Ultra-low-dimensional embeddings for doubling metrics
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Near Optimal Dimensionality Reductions That Preserve Volumes
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Explicit construction of a small epsilon-net for linear threshold functions
Proceedings of the forty-first annual ACM symposium on Theory of computing
Ultra-low-dimensional embeddings for doubling metrics
Journal of the ACM (JACM)
Almost optimal explicit Johnson-Lindenstrauss families
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Deterministic discrepancy minimization
ESA'11 Proceedings of the 19th European conference on Algorithms
Explicit Construction of a Small $\epsilon$-Net for Linear Threshold Functions
SIAM Journal on Computing
Derandomization of dimensionality reduction and SDP based algorithms
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
On approximation algorithms for data mining applications
Efficient Approximation and Online Algorithms
Explicit Dimension Reduction and Its Applications
SIAM Journal on Computing
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The Johnson-Lindenstrauss lemma provides a way to map a number of points in high-dimensional space into a low-dimensional space, with only a small distortion of the distances between the points. The proofs of the lemma are non-constructive: they show that a random mapping induces small distortions with high probability, but they do not construct the actual mapping. In this paper, we provide a procedure that constructs such a mapping deterministically in time almost linear in the number of distances to preserve times the dimension of the original space. We then use that result (together with Nisan's pseudorandom generator) to obtain an efficient derandomization of several approximation algorithms based on semidefinite programming.