### Abstract

We understand selection by intersection as distinguishing a single element of a set by the uniqueness of its occurrence in some other set. More precisely, given two sets A and B, if A ∩ B = {z}, then element z ∈ A is selected by set B. Selectors are such families S of sets B of some domain that allow to select many elements from sufficiently small subsets A of the domain. Selectors are used in communication protocols for the multiple-access channel, in implementations of distributed-computing primitives in radio networks, and in algorithms for group testing. We give new explicit (n, k, r)-selectors of size script O sign(min [n, k^{2}/k-r+1 polylog n]), for any parameters r ≤ k ≤ n. We establish a lower bound Ω(min [n, k^{2}/k-r+1 · log(n/k)/log(k/(k-r+1))]) on the length of (n, k, r)-selectors, which demonstrates that our construction is within a polylog n factor close to optimal. The new selectors are applied to develop explicit implementations of selection resolution on the multiple-access channel, gossiping in radio networks and an algorithm for group testing with inhibitors.

Original language | English (US) |
---|---|

Pages (from-to) | 270-280 |

Number of pages | 11 |

Journal | Lecture Notes in Computer Science |

Volume | 3623 |

State | Published - Oct 24 2005 |

Externally published | Yes |

Event | 15th International Symposium on Fundamentals of Computation Theory, FCT 2005 - Lubeck, Germany Duration: Aug 17 2005 → Aug 20 2005 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science*,

*3623*, 270-280.

**Almost optimal explicit selectors.** / Chlebus, Bogdan S.; Kowalski, Dariusz R.

Research output: Contribution to journal › Conference article

*Lecture Notes in Computer Science*, vol. 3623, pp. 270-280.

}

TY - JOUR

T1 - Almost optimal explicit selectors

AU - Chlebus, Bogdan S.

AU - Kowalski, Dariusz R.

PY - 2005/10/24

Y1 - 2005/10/24

N2 - We understand selection by intersection as distinguishing a single element of a set by the uniqueness of its occurrence in some other set. More precisely, given two sets A and B, if A ∩ B = {z}, then element z ∈ A is selected by set B. Selectors are such families S of sets B of some domain that allow to select many elements from sufficiently small subsets A of the domain. Selectors are used in communication protocols for the multiple-access channel, in implementations of distributed-computing primitives in radio networks, and in algorithms for group testing. We give new explicit (n, k, r)-selectors of size script O sign(min [n, k2/k-r+1 polylog n]), for any parameters r ≤ k ≤ n. We establish a lower bound Ω(min [n, k2/k-r+1 · log(n/k)/log(k/(k-r+1))]) on the length of (n, k, r)-selectors, which demonstrates that our construction is within a polylog n factor close to optimal. The new selectors are applied to develop explicit implementations of selection resolution on the multiple-access channel, gossiping in radio networks and an algorithm for group testing with inhibitors.

AB - We understand selection by intersection as distinguishing a single element of a set by the uniqueness of its occurrence in some other set. More precisely, given two sets A and B, if A ∩ B = {z}, then element z ∈ A is selected by set B. Selectors are such families S of sets B of some domain that allow to select many elements from sufficiently small subsets A of the domain. Selectors are used in communication protocols for the multiple-access channel, in implementations of distributed-computing primitives in radio networks, and in algorithms for group testing. We give new explicit (n, k, r)-selectors of size script O sign(min [n, k2/k-r+1 polylog n]), for any parameters r ≤ k ≤ n. We establish a lower bound Ω(min [n, k2/k-r+1 · log(n/k)/log(k/(k-r+1))]) on the length of (n, k, r)-selectors, which demonstrates that our construction is within a polylog n factor close to optimal. The new selectors are applied to develop explicit implementations of selection resolution on the multiple-access channel, gossiping in radio networks and an algorithm for group testing with inhibitors.

UR - http://www.scopus.com/inward/record.url?scp=26844489396&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26844489396&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:26844489396

VL - 3623

SP - 270

EP - 280

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -