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Algorithms 2016, 9(3), 44; doi:10.3390/a9030044

A Gentle Introduction to Applications of Algorithmic Metatheorems for Space and Circuit Classes

Institute for Theoretical Computer Science, Universität zu Lübeck, Lübeck 23562, Germany
Academic Editor: Henning Fernau
Received: 3 March 2016 / Revised: 24 June 2016 / Accepted: 28 June 2016 / Published: 9 July 2016
View Full-Text   |   Download PDF [582 KB, uploaded 9 July 2016]   |  

Abstract

Algorithmic metatheorems state that if a problem can be described in a certain logic and the inputs are structured in a certain way, then the problem can be solved with a certain amount of resources. As an example, by Courcelle’s Theorem, all monadic second-order (“in a certain logic”) properties of graphs of bounded tree width (“structured in a certain way”) can be solved in linear time (“with a certain amount of resources”). Such theorems have become valuable tools in algorithmics: if a problem happens to have the right structure and can be described in the right logic, they immediately yield a (typically tight) upper bound on the time complexity of the problem. Perhaps even more importantly, several complex algorithms rely on algorithmic metatheorems internally to solve subproblems, which considerably broadens the range of applications of these theorems. This paper is intended as a gentle introduction to the ideas behind algorithmic metatheorems, especially behind some recent results concerning space and circuit classes, and tries to give a flavor of the range of their applications. View Full-Text
Keywords: algorithmic metatheorems; Courcelle’s Theorem; tree width; tree depth; monadic second-order logic; logarithmic space; circuit classes algorithmic metatheorems; Courcelle’s Theorem; tree width; tree depth; monadic second-order logic; logarithmic space; circuit classes
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Tantau, T. A Gentle Introduction to Applications of Algorithmic Metatheorems for Space and Circuit Classes. Algorithms 2016, 9, 44.

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