Space-Optimal Quasi-Gray Codes with Logarithmic Read Complexity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10387302" target="_blank" >RIV/00216208:11320/18:10387302 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.ESA.2018.12" target="_blank" >https://doi.org/10.4230/LIPIcs.ESA.2018.12</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ESA.2018.12" target="_blank" >10.4230/LIPIcs.ESA.2018.12</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Space-Optimal Quasi-Gray Codes with Logarithmic Read Complexity

Popis výsledku v původním jazyce

A quasi-Gray code of dimension n and length l over an alphabet Sigma is a sequence of distinct words w_1,w_2,...,w_l from Sigma^n such that any two consecutive words differ in at most c coordinates, for some fixed constant c&gt;0. In this paper we are interested in the read and write complexity of quasi-Gray codes in the bit-probe model, where we measure the number of symbols read and written in order to transform any word w_i into its successor w_{i+1}. We present construction of quasi-Gray codes of dimension n and length 3^n over the ternary alphabet {0,1,2} with worst-case read complexity O(log n) and write complexity 2. This generalizes to arbitrary odd-size alphabets. For the binary alphabet, we present quasi-Gray codes of dimension n and length at least 2^n - 20n with worst-case read complexity 6+log n and write complexity 2. This complements a recent result by Raskin [Raskin &apos;17] who shows that any quasi-Gray code over binary alphabet of length 2^n has read complexity Omega(n). Our results significantly improve on previously known constructions and for the odd-size alphabets we break the Omega(n) worst-case barrier for space-optimal (non-redundant) quasi-Gray codes with constant number of writes. We obtain our results via a novel application of algebraic tools together with the principles of catalytic computation [Buhrman et al. &apos;14, Ben-Or and Cleve &apos;92, Barrington &apos;89, Coppersmith and Grossman &apos;75].

Název v anglickém jazyce

Space-Optimal Quasi-Gray Codes with Logarithmic Read Complexity

Popis výsledku anglicky

A quasi-Gray code of dimension n and length l over an alphabet Sigma is a sequence of distinct words w_1,w_2,...,w_l from Sigma^n such that any two consecutive words differ in at most c coordinates, for some fixed constant c&gt;0. In this paper we are interested in the read and write complexity of quasi-Gray codes in the bit-probe model, where we measure the number of symbols read and written in order to transform any word w_i into its successor w_{i+1}. We present construction of quasi-Gray codes of dimension n and length 3^n over the ternary alphabet {0,1,2} with worst-case read complexity O(log n) and write complexity 2. This generalizes to arbitrary odd-size alphabets. For the binary alphabet, we present quasi-Gray codes of dimension n and length at least 2^n - 20n with worst-case read complexity 6+log n and write complexity 2. This complements a recent result by Raskin [Raskin &apos;17] who shows that any quasi-Gray code over binary alphabet of length 2^n has read complexity Omega(n). Our results significantly improve on previously known constructions and for the odd-size alphabets we break the Omega(n) worst-case barrier for space-optimal (non-redundant) quasi-Gray codes with constant number of writes. We obtain our results via a novel application of algebraic tools together with the principles of catalytic computation [Buhrman et al. &apos;14, Ben-Or and Cleve &apos;92, Barrington &apos;89, Coppersmith and Grossman &apos;75].

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název statě ve sborníku

26th Annual European Symposium on Algorithms, {ESA} 2018, August 20-22, 2018, Helsinki, Finland

ISBN

978-3-95977-081-1

ISSN

—

e-ISSN

neuvedeno

Počet stran výsledku

15

Strana od-do

1-15

Název nakladatele

Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik

Místo vydání

Schloss Dagstuhl, Germany

Místo konání akce

Helsinki, Finland

Datum konání akce

20. 8. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—