Witness sets for families of binary vectors

Eyal Kushilevitz*, Nathan Linial, Yuri Rabinovich, Michael Saks

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

Given a family ℛ ⊆ {0, 1} m of binary vectors of length m, a set W ⊆ {1,...,m} is called a witness set for r ∈ ℛ, if for all other r′ ∈ ℛ there exists a coordinate c ∈ W such that rc ≠ r′c. The smallest cardinality of a witness set for r ∈ ℛ is denoted w(r) = w (r). In this note we show that Σr∈ℛ w(r) = O(|ℛ|3/2) and constructions are given to show that this bound is tight. Further information is derived on the distribution of values of {w(r)|r ∈ ℛ}.

Original languageAmerican English
Pages (from-to)376-380
Number of pages5
JournalJournal of Combinatorial Theory. Series A
Volume73
Issue number2
DOIs
StatePublished - 1996

Bibliographical note

Funding Information:
Let N _ { 0, I } "' be a family of distinct binary vectors of length m. A set W_ \[m\] of coordinates is a witness set for a vector r in ~, if for every * E-maih eyalk@cs.technion.ac.il. t Work supported in part by a grant from the Israeli Academy of Sciences. E-maih nati@huji.ac.il. t Supported in part by NSF Contract CCR-9215293 and by DIMACS, which is partially funded by NSF Grant STC-91-19999, and the NJ Comission of Science and Technology.

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