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Splitters and near-optimal derandomization
- M. Naor, L. Schulman, A. Srinivasan
- Computer Science, MathematicsProceedings of IEEE 36th Annual Foundations of…
- 23 October 1995
A fairly general method for finding deterministic constructions obeying k-restrictions, which yields structures of size not much larger than the probabilistic bound and imply the very efficient derandomization of algorithms in learning, of fixed-subgraph finding algorithms, and of near optimal /spl Sigma/II/Spl Sigma/ threshold formulae.
The Effectiveness of Lloyd-Type Methods for the k-Means Problem
- R. Ostrovsky, Y. Rabani, L. Schulman, Chaitanya Swamy
- Computer ScienceIEEE Annual Symposium on Foundations of Computer…
- 21 October 2006
This work investigates variants of Lloyd's heuristic for clustering high dimensional data in an attempt to explain its popularity (a half century after its introduction) among practitioners, and proposes and justifies a clusterability criterion for data sets.
Coding for interactive communication
- L. Schulman
- Computer ScienceProceedings of IEEE International Symposium on…
- 17 September 1995
A deterministic method for simulating noiseless-channel protocols on noisy channels, with only a constant slowdown is described, an analog for general, interactive protocols of Shannon's coding theorem, which deals only with data transmission, i.e., one-way protocols.
Broadcasting on trees and the Ising model
Consider a process in which information is transmitted from a given root node on a noisy tree network T . We start with an unbiased random bit R at the root of the tree and send it down the edges of…
A coding theorem for distributed computation
- S. Rajagopalan, L. Schulman
- Computer Science, MathematicsSymposium on the Theory of Computing
- 23 May 1994
It is shown that any distributed protocol which runs on a noiseless network in time T, can be simulated on an identical noisy network with a slow-down factor proportional to log(d + 1), where d is the maximum degree in the network, and with exponentially small probability of error.
Communication on noisy channels: a coding theorem for computation
- L. Schulman
- Computer ScienceProceedings., 33rd Annual Symposium on…
- 24 October 1992
The author relates the noisy channel and the standard (noise less channel) complexities of a communication problem by establishing a 'two-way' or interactive analogue of Shanon's coding theorem, which involves simulating the original protocol while implementing a hierarchical system of progress checks which ensure that errors of any magnitude in the simulation are, with high probability, rapidly eliminated.
Quantum mechanical algorithms for the nonabelian hidden subgroup problem
- M. Grigni, L. Schulman, M. Vazirani, U. Vazirani
- MathematicsSymposium on the Theory of Computing
- 6 July 2001
We provide positive and negative results concerning the “standard method” of identifying a hidden subgroup of a nonabelian group using a quantum computer.
Deterministic coding for interactive communication
- L. Schulman
- Computer ScienceSymposium on the Theory of Computing
- 1 June 1993
A deterministic method for simulating noiseless-channel protocols on noisy channels, with only a constant slow-down is described, an analog for general interactive protocols of Shannon's coding theorem, which dealt only with data transmission, i.e. one-way protocols.
Lower bounds for linear locally decodable codes and private information retrieval
- Oded Goldreich, H. Karloff, L. Schulman, L. Trevisan
- Computer ScienceProceedings 17th IEEE Annual Conference on…
- 21 May 2002
It is shown a reduction from the complexity of one-round, information-theoretic Private Information Retrieval Systems (with two servers) to Locally Decodable Codes, and it is proved that if all the servers’ answers are linear combinations of the database content, then t = Ω (n/2a), where t is the length of the user’s query.
A Probabilistic Analysis of EM for Mixtures of Separated, Spherical Gaussians
We show that, given data from a mixture of k well-separated spherical Gaussians in ℜd, a simple two-round variant of EM will, with high probability, learn the parameters of the Gaussians to…