Bounds on universal sequences

Amotz Bar-Noy; Allan Borodin; Mauricio Karchmer; Nathan Linial; Michael Werman

doi:10.1137/0218018

Bounds on universal sequences

Amotz Bar-Noy^*, Allan Borodin, Mauricio Karchmer, Nathan Linial, Michael Werman

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Universal sequences for graphs are studied. By letting U(d, n) denote the minimum length of a universal sequence for d-regular undirected graphs with n nodes, the latter paper has proved the upper bound U(d, n) = O(d²n³ log n) using a probabilistic argument. Here a lower bound of U(2, n) = Ω(n log n) is proved from which U(d, n) = Ω(n log n) for all d is deduced. Also, for complete graphs U(n - 1, n) = Ω(n log² n/log n). An explicit construction of universal sequences for cycles (d = 2) of length n^{O(log n)} is given.

Original language	English
Pages (from-to)	268-277
Number of pages	10
Journal	SIAM Journal on Computing
Volume	18
Issue number	2
DOIs	https://doi.org/10.1137/0218018
State	Published - 1989

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title = "Bounds on universal sequences",

abstract = "Universal sequences for graphs are studied. By letting U(d, n) denote the minimum length of a universal sequence for d-regular undirected graphs with n nodes, the latter paper has proved the upper bound U(d, n) = O(d2n3 log n) using a probabilistic argument. Here a lower bound of U(2, n) = Ω(n log n) is proved from which U(d, n) = Ω(n log n) for all d is deduced. Also, for complete graphs U(n - 1, n) = Ω(n log2 n/log n). An explicit construction of universal sequences for cycles (d = 2) of length nO(log n) is given.",

author = "Amotz Bar-Noy and Allan Borodin and Mauricio Karchmer and Nathan Linial and Michael Werman",

year = "1989",

doi = "10.1137/0218018",

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T1 - Bounds on universal sequences

AU - Bar-Noy, Amotz

AU - Borodin, Allan

AU - Karchmer, Mauricio

AU - Linial, Nathan

AU - Werman, Michael

PY - 1989

Y1 - 1989

N2 - Universal sequences for graphs are studied. By letting U(d, n) denote the minimum length of a universal sequence for d-regular undirected graphs with n nodes, the latter paper has proved the upper bound U(d, n) = O(d2n3 log n) using a probabilistic argument. Here a lower bound of U(2, n) = Ω(n log n) is proved from which U(d, n) = Ω(n log n) for all d is deduced. Also, for complete graphs U(n - 1, n) = Ω(n log2 n/log n). An explicit construction of universal sequences for cycles (d = 2) of length nO(log n) is given.

AB - Universal sequences for graphs are studied. By letting U(d, n) denote the minimum length of a universal sequence for d-regular undirected graphs with n nodes, the latter paper has proved the upper bound U(d, n) = O(d2n3 log n) using a probabilistic argument. Here a lower bound of U(2, n) = Ω(n log n) is proved from which U(d, n) = Ω(n log n) for all d is deduced. Also, for complete graphs U(n - 1, n) = Ω(n log2 n/log n). An explicit construction of universal sequences for cycles (d = 2) of length nO(log n) is given.

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SN - 0097-5397

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JO - SIAM Journal on Computing

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Bounds on universal sequences

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