Space-Optimal Quasi-Gray Codes with Logarithmic Read Complexity
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Space-Optimal Quasi-Gray Codes with Logarithmic Read Complexity
Original language description
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>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 '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. '14, Ben-Or and Cleve '92, Barrington '89, Coppersmith and Grossman '75].
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
26th Annual European Symposium on Algorithms, {ESA} 2018, August 20-22, 2018, Helsinki, Finland
ISBN
978-3-95977-081-1
ISSN
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e-ISSN
neuvedeno
Number of pages
15
Pages from-to
1-15
Publisher name
Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik
Place of publication
Schloss Dagstuhl, Germany
Event location
Helsinki, Finland
Event date
Aug 20, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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