Improved methods for generating quasi-gray codes

Prosenjit Bose; Paz Carmi; Dana Jansens; Anil Maheshwari; Pat Morin; Michiel Smid

doi:10.1007/978-3-642-13731-0_22

Improved methods for generating quasi-gray codes

Prosenjit Bose
, Paz Carmi
, Dana Jansens
, Anil Maheshwari
, Pat Morin
, Michiel Smid

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 Scopus citations

Abstract

Consider a sequence of bit strings of length d, such that each string differs from the next in a constant number of bits. We call this sequence a quasi-Gray code. We examine the problem of efficiently generating such codes, by considering the number of bits read and written at each generating step, the average number of bits read while generating the entire code, and the number of strings generated in the code. Our results give a trade-off between these constraints, and present algorithms that do less work on average than previous results, and that increase the number of bit strings generated.

Original language	English
Title of host publication	Algorithm Theory - SWAT 2010 - 12th Scandinavian Symposium and Workshops on Algorithm Theory, Proceedings
Pages	224-235
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-13731-0_22
State	Published - 21 Jul 2010
Event	12th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2010 - Bergen, Norway Duration: 21 Jun 2010 → 23 Jun 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6139 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2010
Country/Territory	Norway
City	Bergen
Period	21/06/10 → 23/06/10

Keywords

Gray codes
combinatorial generation
counting
decision trees
quasi-Gray codes

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-13731-0_22

Cite this

Bose, P., Carmi, P., Jansens, D., Maheshwari, A., Morin, P., & Smid, M. (2010). Improved methods for generating quasi-gray codes. In Algorithm Theory - SWAT 2010 - 12th Scandinavian Symposium and Workshops on Algorithm Theory, Proceedings (pp. 224-235). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6139 LNCS). https://doi.org/10.1007/978-3-642-13731-0_22

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title = "Improved methods for generating quasi-gray codes",

abstract = "Consider a sequence of bit strings of length d, such that each string differs from the next in a constant number of bits. We call this sequence a quasi-Gray code. We examine the problem of efficiently generating such codes, by considering the number of bits read and written at each generating step, the average number of bits read while generating the entire code, and the number of strings generated in the code. Our results give a trade-off between these constraints, and present algorithms that do less work on average than previous results, and that increase the number of bit strings generated.",

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author = "Prosenjit Bose and Paz Carmi and Dana Jansens and Anil Maheshwari and Pat Morin and Michiel Smid",

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Bose, P, Carmi, P, Jansens, D, Maheshwari, A, Morin, P & Smid, M 2010, Improved methods for generating quasi-gray codes. in Algorithm Theory - SWAT 2010 - 12th Scandinavian Symposium and Workshops on Algorithm Theory, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6139 LNCS, pp. 224-235, 12th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2010, Bergen, Norway, 21/06/10. https://doi.org/10.1007/978-3-642-13731-0_22

Improved methods for generating quasi-gray codes. / Bose, Prosenjit; Carmi, Paz; Jansens, Dana et al.
Algorithm Theory - SWAT 2010 - 12th Scandinavian Symposium and Workshops on Algorithm Theory, Proceedings. 2010. p. 224-235 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6139 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Smid, Michiel

PY - 2010/7/21

Y1 - 2010/7/21

N2 - Consider a sequence of bit strings of length d, such that each string differs from the next in a constant number of bits. We call this sequence a quasi-Gray code. We examine the problem of efficiently generating such codes, by considering the number of bits read and written at each generating step, the average number of bits read while generating the entire code, and the number of strings generated in the code. Our results give a trade-off between these constraints, and present algorithms that do less work on average than previous results, and that increase the number of bit strings generated.

AB - Consider a sequence of bit strings of length d, such that each string differs from the next in a constant number of bits. We call this sequence a quasi-Gray code. We examine the problem of efficiently generating such codes, by considering the number of bits read and written at each generating step, the average number of bits read while generating the entire code, and the number of strings generated in the code. Our results give a trade-off between these constraints, and present algorithms that do less work on average than previous results, and that increase the number of bit strings generated.

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KW - counting

KW - decision trees

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Bose P, Carmi P, Jansens D, Maheshwari A, Morin P, Smid M. Improved methods for generating quasi-gray codes. In Algorithm Theory - SWAT 2010 - 12th Scandinavian Symposium and Workshops on Algorithm Theory, Proceedings. 2010. p. 224-235. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-13731-0_22

Improved methods for generating quasi-gray codes

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Keywords

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