A Lower Bound on CNF Encodings of the At-most-one Constraint

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00494392" target="_blank" >RIV/67985807:_____/19:00494392 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/19:10402518

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.tcs.2018.09.003" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2018.09.003</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.tcs.2018.09.003" target="_blank" >10.1016/j.tcs.2018.09.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Lower Bound on CNF Encodings of the At-most-one Constraint

Popis výsledku v původním jazyce

Constraint 'at most one' is a basic cardinality constraint which requires that at most one of its n boolean inputs is set to 1. This constraint is widely used when translating a problem into a conjunctive normal form (CNF) and we investigate its CNF encodings suitable for this purpose. An encoding differs from a CNF representation of a function in that it can use auxiliary variables. We are especially interested in propagation complete encodings which have the property that unit propagation is strong enough to enforce consistency on input variables. We show a lower bound on the number of clauses in any propagation complete encoding of the 'at most one' constraint. The lower bound almost matches the size of the best known encodings. We also study an important case of 2-CNF encodings where we show a slightly better lower bound. The lower bound holds also for a related 'exactly one' constraint.

Název v anglickém jazyce

A Lower Bound on CNF Encodings of the At-most-one Constraint

Popis výsledku anglicky

Constraint 'at most one' is a basic cardinality constraint which requires that at most one of its n boolean inputs is set to 1. This constraint is widely used when translating a problem into a conjunctive normal form (CNF) and we investigate its CNF encodings suitable for this purpose. An encoding differs from a CNF representation of a function in that it can use auxiliary variables. We are especially interested in propagation complete encodings which have the property that unit propagation is strong enough to enforce consistency on input variables. We show a lower bound on the number of clauses in any propagation complete encoding of the 'at most one' constraint. The lower bound almost matches the size of the best known encodings. We also study an important case of 2-CNF encodings where we show a slightly better lower bound. The lower bound holds also for a related 'exactly one' constraint.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

—

Svazek periodika

762

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

23

Strana od-do

51-73

Kód UT WoS článku

000459528200005

EID výsledku v databázi Scopus

2-s2.0-85053701165