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(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 language | English |
|---|---|
| Pages (from-to) | 376-380 |
| Number of pages | 5 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 73 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1996 |
| Externally published | Yes |
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 [email protected]. t Work supported in part by a grant from the Israeli Academy of Sciences. E-maih [email protected]. 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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics