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Electronic Colloquium on Computational Complexity

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Reports tagged with Probabilistic Algorithms:
TR95-058 | 20th November 1995
Amnon Ta-Shma

On Extracting Randomness From Weak Random Sources

We deal with the problem of extracting as much randomness as possible
from a defective random source.
We devise a new tool, a ``merger'', which is a function that accepts
d strings, one of which is uniformly distributed,
and outputs a single string that is guaranteed ... more >>>

TR96-029 | 16th April 1996
Alexander E. Andreev, Andrea E. F. Clementi, Jose' D. P. Rolim

Towards efficient constructions of hitting sets that derandomize BPP

The efficient construction of Hitting Sets for non trivial classes
of boolean functions is a fundamental problem in the theory
of derandomization. Our paper presents a new method to efficiently
construct Hitting Sets for the class of systems of boolean linear
functions. Systems of boolean linear functions ... more >>>

TR00-060 | 17th August 2000
Uri Zwick

All Pairs Shortest Paths using Bridging Sets and Rectangular Matrix Multiplication

We present two new algorithms for solving the {\em All
Pairs Shortest Paths\/} (APSP) problem for weighted directed
graphs. Both algorithms use fast matrix multiplication algorithms.

The first algorithm
solves the APSP problem for weighted directed graphs in which the edge
weights are integers of small absolute value in ... more >>>

TR17-036 | 22nd February 2017
Dean Doron, Francois Le Gall, Amnon Ta-Shma

Probabilistic logarithmic-space algorithms for Laplacian solvers

A recent series of breakthroughs initiated by Spielman and Teng culminated in the construction of nearly linear time Laplacian solvers, approximating the solution of a linear system $L x=b$, where $L$ is the normalized Laplacian of an undirected graph. In this paper we study the space complexity of the problem.
more >>>

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