Optimal conclusive sets for comparator networks

Guy Even*, Tamir Levi, Ami Litman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A set of input vectors S is conclusive if correct functionality for all input vectors is implied by correct functionality over vectors in S. We consider four functionalities of comparator networks: sorting, merging of two equal length sorted vectors, sorting of bitonic vectors, and halving (i.e., separating values above and below the median). For each of these functionalities, we present tight lower and upper bounds on the size of conclusive sets. Bounds are given both for conclusive sets composed of binary vectors and of general vectors. The bounds for general vectors are smaller than the bounds for binary vectors implied by the 0-1 principle. Our results hold also for comparator networks with unbounded fanout. Assume the network at hand has n inputs and outputs, where n is even. We present a conclusive set for sorting that contains (n/2n) nonbinary vectors. For merging, we present a conclusive set with n/2 + 1 nonbinary vectors. For bitonic sorting, we present a conclusive set with n nonbinary vectors. For halving, we present ( n/2n) binary vectors that constitute a conclusive set. We prove that all these conclusive sets are optimal.

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 14th International Colloquium, SIROCCO 2007, Proceedings
PublisherSpringer Verlag
Pages304-317
Number of pages14
ISBN (Print)9783540729181
DOIs
StatePublished - 2007
Event14th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2007 - Castiglioncello, Italy
Duration: 5 Jun 20078 Jun 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4474 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2007
Country/TerritoryItaly
CityCastiglioncello
Period5/06/078/06/07

Keywords

  • Bitonic sorting
  • Comparator networks
  • Merging networks
  • Sorting networks
  • Zero-one principle

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