Counting Distinct Elements in a Data Stream
- Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, D. Sivakumar, L. Trevisan
- Computer ScienceInternational Workshop Randomization and…
- 13 September 2002
We present three algorithms to count the number of distinct elements in a data stream to within a factor of 1 ± ?. Our algorithms improve upon known algorithms for this problem, and offer a spectrum…
On the efficiency of local decoding procedures for error-correcting codes
In appli ations to data storage (and also in applications to data transmission) a message is typi ally into small blo ks, and then ea h blo k is en oded separately, which allows retrieval of data stored in musi CDs and in CD-ROMs.
Extractors and pseudorandom generators
- L. Trevisan
- Mathematics, Computer ScienceJACM
It is shown that, using the simpler Nisan--Wigderson generator and standard error-correcting codes, one can build even better extractors with the additional advantage that both the construction and the analysis are simple and admit a short self-contained description.
Pseudorandom generators without the XOR Lemma
Two different approaches are presented to proving the main result of Impagliazzo and Wigderson that if there exists a decision problem solvable in time 2/sup O(n)/ and having circuit complexity 2/Sup /spl Omega/(n)/ then P=BPP.
Lower bounds on the efficiency of generic cryptographic constructions
- R. Gennaro, L. Trevisan
- Computer Science, MathematicsProceedings 41st Annual Symposium on Foundations…
- 12 November 2000
This paper gives lower bounds on the number of invocations to the oracle by the PRG construction based on black-box access to one-way permutations and proves that a proof of the existence of PRG (resp. UOWHF) black- box constructions that beat the lower bound would imply aProof of the unconditional existence of such construction (which would also imply P/spl ne/NP).
Multi-way spectral partitioning and higher-order cheeger inequalities
This work shows that in every graph there are at least k/2 disjoint sets, each having expansion at most O(√(λk log k), and proves that the √(log k) bound is tight, up to constant factors, for the "noisy hypercube" graphs.
Non-approximability results for optimization problems on bounded degree instances
- L. Trevisan
- MathematicsSymposium on the Theory of Computing
- 6 July 2001
Some non-approximability results for restrictions of basic combinatorial optimization problems to instances of bounded “degree” or bounded ”width” are proved.
A PCP characterization of NP with optimal amortized query complexity
- Alex Samorodnitsky, L. Trevisan
- Computer Science, MathematicsSymposium on the Theory of Computing
- 1 May 2000
It is shown that k-CSP, the problem of finding an assignment satisfying the maximum number of given constraints (where each constraint involves at most k variables) is NP-hard to approximate to within a factor 2 √ .
Gadgets, approximation, and linear programming
- L. Trevisan, G. Sorkin, M. Sudan, David P. Williamson
- Computer ScienceProceedings of 37th Conference on Foundations of…
- 14 October 1996
The authors present a linear-programming based method for finding "gadgets", i.e., combinatorial structures reducing constraints of one optimization problem to constraints of another. A key step in…
The Approximability of Constraint Satisfaction Problems
- S. Khanna, M. Sudan, L. Trevisan, David P. Williamson
- Computer ScienceSIAM journal on computing (Print)
- 1 December 2001
Tight bounds on the "approximability" of every problem in Max Ones, Min CSP, and Min Ones are determined and this completely classifies all optimization problems derived from Boolean constraint satisfaction.