License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2020.1
URN: urn:nbn:de:0030-drops-121261
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12126/
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Husfeldt, Thore

Algebraic Algorithms for Finding Patterns in Graphs (Invited Talk)

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LIPIcs-CPM-2020-1.pdf (0.2 MB)

Abstract

I will give a gentle introduction to algebraic graph algorithms by showing how to determine if a given graph contains a simple path of length k. This is a famous problem admitting a beautiful and widely-known algorithm, namely the colour-coding method of Alon, Yuster and Zwick (1995). Starting from this entirely combinatorial approach, I will carefully develop an algebraic perspective on the same problem. First, I will explain how the colour-coding algorithm can be understood as the evaluation of a well-known expression (sometimes called the "walk-sum" of the graph) in a commutative algebra called the zeon algebra. From there, I will introduce the exterior algebra and present the algebraic framework recently developed with Brand and Dell (2018).
The presentation is aimed at a combinatorially-minded audience largely innocent of abstract algebra.

BibTeX - Entry

@InProceedings{husfeldt:LIPIcs:2020:12126,
  author =	{Thore Husfeldt},
  title =	{{Algebraic Algorithms for Finding Patterns in Graphs (Invited Talk)}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{Inge Li G{\o}rtz and Oren Weimann},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12126},
  URN =		{urn:nbn:de:0030-drops-121261},
  doi =		{10.4230/LIPIcs.CPM.2020.1},
  annote =	{Keywords: paths, exterior algebra, wedge product, color-coding, parameterized complexity}
}

Keywords: paths, exterior algebra, wedge product, color-coding, parameterized complexity
Collection: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
Issue Date: 2020
Date of publication: 09.06.2020

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