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- Moni Naor, Leonard J. Schulman, Aravind Srinivasan
- FOCS
- 1995

We present a fairly general method for nding deterministic constructions obeying what we call k-restrictions; this yields structures of size not much larger than the probabilistic bound. The structures constructed by our method include (n; k)-universal sets (a collection of binary vectors of length n such that for any subset of size k of the indices, all 2… (More)

- Oded Goldreich, Howard J. Karloff, Leonard J. Schulman, Luca Trevisan
- Computational Complexity
- 2001

We prove that if a linear error-correcting code C : f0;1g n ! f0;1g m is such that a bit of the message can be probabilistically reconstructed by looking at two entries of a corrupted codeword, then m = 2 (n). We also present several extensions of this result. We show a reduction from the complexity of one-round, information-theoretic Private Information… (More)

- Rafail Ostrovsky, Yuval Rabani, Leonard J. Schulman, Chaitanya Swamy
- 2006 47th Annual IEEE Symposium on Foundations of…
- 2006

We investigate 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 in order to suggest improvements in its application. We propose and justify a <i>clusterability</i> criterion for data sets. We present variants of Lloyd's heuristic that… (More)

- Leonard J. Schulman
- IEEE Trans. Information Theory
- 1996

Let the input to a computation problem be split between two processors connected by a communication link; and let an interactive protocol be known by which, on any input, the processors can solve the problem using no more than T transmissions of bits between them, provided the channel is noiseless in each direction. We study the following question: if in… (More)

In this paper we obtain improved upper and lower bounds for the best approximation factor for Sparsest Cut achievable in the cut-matching game framework proposed in Khandekar et al. [9]. We show that this simple framework can be used to design combinatorial algorithms that achieve O(log n) approximation factor and whose running time is dominated by a… (More)

- Leonard J. Schulman
- FOCS
- 1992

- Sridhar Rajagopalan, Leonard J. Schulman
- STOC
- 1994

1 Introduction This paper is concerned with the question of whether it is possible to sustain computation in the presence of noise; and if so, at what cost in efficiency and reliability. Shannon in his classical coding theorem showed that data can successfully and efficiently be transmitted in a noisy environment [27]. The outstanding features of the… (More)

- William S. Evans, Leonard J. Schulman
- IEEE Trans. Information Theory
- 2003

— We determine the precise threshold of component noise below which formulas composed of odd degree components can reliably compute all Boolean functions.

- Leonard J. Schulman
- STOC
- 1993

Two factors are prominent among those contributing to the increases in speed and storage capacity in current generations of computers. The first is increasing parallelism — whether in actual parallel and distributed computers, or among the steadily more numerous components of a sequential machine. The second is the dramatic miniaturization of logical… (More)

We provide positive and negative results concerning the “standard method” of identifying a hidden subgroup of a nonabelian group using a quantum computer.