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Spring 2010 Sublinear time algorithms in the theory of groups and semigroups
Vladimir Shpilrain
Illinois J. Math. 54(1): 187-197 (Spring 2010). DOI: 10.1215/ijm/1299679745


Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a small portion of the input. The most typical situation where sublinear time algorithms are considered is property testing. There are several interesting contexts where one can test properties in sublinear time. A canonical example is graph colorability. To tell that a given graph is not $k$-colorable, it is often sufficient to inspect just one vertex with incident edges: if the degree of a vertex is greater than $k$, then the graph is not $k$-colorable.

It is a challenging and interesting task to find algebraic properties that could be tested in sublinear time. In this paper, we address several algorithmic problems in the theory of groups and semigroups that may admit sublinear time solution, at least for “most” inputs.


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Vladimir Shpilrain. "Sublinear time algorithms in the theory of groups and semigroups." Illinois J. Math. 54 (1) 187 - 197, Spring 2010.


Published: Spring 2010
First available in Project Euclid: 9 March 2011

zbMATH: 1234.20044
MathSciNet: MR2776992
Digital Object Identifier: 10.1215/ijm/1299679745

Primary: 20F10, 68Q17
Secondary: 20M05, 68W30

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign


Vol.54 • No. 1 • Spring 2010
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