TY - GEN

T1 - Derandomizing Algorithms on Product Distributions and Other Applications of Order-Based Extraction

AU - Gabizon, Ariel

AU - Hassidim, A.

N1 - Place of conference:China

PY - 2010

Y1 - 2010

N2 - Getting the deterministic complexity closer to the best known randomized complexity is an important
goal in algorithms and communication protocols. In this work, we investigate the case where
instead of one input, the algorithm/protocol is given multiple inputs sampled independently from
an arbitrary unknown distribution. We show that in this case a strong and generic derandomization
result can be obtained by a simple argument.
Our method relies on extracting randomness from “same-source” product distributions, which
are distributions generated from multiple independent samples from the same source. The extraction
process succeeds even for arbitrarily low min-entropy, and is based on the order of the values and
not on the values themselves (this may be seen as a generalization of the classical method of VonNeumann
[26] extended by Elias [7] for extracting randomness from a biased coin.)
The tools developed in the paper are generic, and can be used in several other problems. We
present applications to streaming algorithms, and to implicit probe search [8]. We also refine our
method to handle product distributions, where the i'th sample comes from one of several arbitrary
unknown distributions. This requires creating a new set of tools, which may also be of independent
interest.

AB - Getting the deterministic complexity closer to the best known randomized complexity is an important
goal in algorithms and communication protocols. In this work, we investigate the case where
instead of one input, the algorithm/protocol is given multiple inputs sampled independently from
an arbitrary unknown distribution. We show that in this case a strong and generic derandomization
result can be obtained by a simple argument.
Our method relies on extracting randomness from “same-source” product distributions, which
are distributions generated from multiple independent samples from the same source. The extraction
process succeeds even for arbitrarily low min-entropy, and is based on the order of the values and
not on the values themselves (this may be seen as a generalization of the classical method of VonNeumann
[26] extended by Elias [7] for extracting randomness from a biased coin.)
The tools developed in the paper are generic, and can be used in several other problems. We
present applications to streaming algorithms, and to implicit probe search [8]. We also refine our
method to handle product distributions, where the i'th sample comes from one of several arbitrary
unknown distributions. This requires creating a new set of tools, which may also be of independent
interest.

UR - https://scholar.google.co.il/scholar?q=Derandomizing+Algorithms+on+Product+Distributions+and+Other+Applications+of+Order-Based+Extraction&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

BT - ICS

ER -