An improved analysis of mergers

Zeev Dvir*, Amir Shpilka

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


Mergers are functions that transform k (possibly dependent) random sources into a single random source, in a way that ensures that if one of the input sources has min-entropy rate δ then the output has min-entropy rate close to δ. Mergers have proven to be a very useful tool in explicit constructions of extractors and condensers, and are also interesting objects in their own right. In this work we present a new analysis of the merger construction of [6]. Our analysis shows that the min-entropy rate of this merger's output is actually 0.52 · δ instead of 0.5·δ, where δ is the min-entropy rate of one of the inputs. To obtain this result we deviate from the usual linear algebra methods that were used by [6] and introduce a new technique that involves results from additive number theory.

Original languageEnglish
Pages (from-to)270-281
Number of pages12
JournalLecture Notes in Computer Science
StatePublished - 2005
Externally publishedYes
Event8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005 - Berkeley, CA, United States
Duration: 22 Aug 200524 Aug 2005


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