Triangle Counting in Dynamic Graph Streams

Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in an arbitrary order or as incidence lists. However, with a fe...

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Vydáno v:Algorithmica Ročník 76; číslo 1; s. 259 - 278
Hlavní autoři: Bulteau, Laurent, Froese, Vincent, Kutzkov, Konstantin, Pagh, Rasmus
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.09.2016
Springer Verlag
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Bioinformatics
Computational Complexity
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Algorithms
Data Structures and Information Theory
Mathematics of Computing
Theory of Computation
Streaming algorithms
Triangle counting
Randomized approximation algorithms
ISSN:0178-4617, 1432-0541
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Shrnutí:Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in an arbitrary order or as incidence lists. However, with a few exceptions, the algorithms have considered insert-only streams. We present a new algorithm estimating the number of triangles in dynamic graph streams where edges can be both inserted and deleted. We show that our algorithm achieves better time and space complexity than previous solutions for various graph classes, for example sparse graphs with a relatively small number of triangles. Also, for graphs with constant transitivity coefficient, a common situation in real graphs, this is the first algorithm achieving constant processing time per edge. The result is achieved by a novel approach combining sampling of vertex triples and sparsification of the input graph. In the course of the analysis of the algorithm we present a lower bound on the number of pairwise independent 2-paths in general graphs which might be of independent interest. At the end of the paper we discuss lower bounds on the space complexity of triangle counting algorithms that make no assumptions on the structure of the graph.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-015-0036-4