Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
Random projection in dimensionality reduction: applications to image and text data
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Pass efficient algorithms for approximating large matrices
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Euclidean Embeddings and Bandwidth Minimization
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
An Algorithmic Theory of Learning: Robust Concepts and Random Projection
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Virtual coordinates for ad hoc and sensor networks
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Volume distortion for subsets of Euclidean spaces: extended abstract
Proceedings of the twenty-second annual symposium on Computational geometry
Very sparse random projections
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
New theoretical results on quadratic placement
Integration, the VLSI Journal
Very sparse stable random projections for dimension reduction in lα (0
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
European Journal of Combinatorics
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
FPGA placement using space-filling curves: Theory meets practice
ACM Transactions on Embedded Computing Systems (TECS)
Good quality virtual realization of unit ball graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Sensor networks continue to puzzle: selected open problems
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
Random projection, margins, kernels, and feature-selection
SLSFS'05 Proceedings of the 2005 international conference on Subspace, Latent Structure and Feature Selection
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We show that Random Projection, the technique of projecting a set of points to a randomly chosen low-dimensional subspace, can be used to solve problems in VLSI layout. Specifically, for the problem of laying out a graph on a 2-dimensional grid so as to minimize the maximum edge length, we obtain an O(log^{3.5} n) approximation algorithm (this is the first o(n) approximation), and for the bicriteria problem of minimizing the total edge length while keeping the maximum length bounded, we obtain an O(log^3 n, log^{3.5} n) approximation. Our algorithms also work for d-dimensional versions of these problems (for any fixed d) with polylog approximation guarantees. Besides random projection, the main components of the algorithms are a linear programming relaxation, and volume-respecting Euclidean embeddings (introduced by Feige).