Triangle Counting in Dynamic Graph Streams

被引:19
|
作者
Bulteau, Laurent [1 ,4 ]
Froese, Vincent [1 ]
Kutzkov, Konstantin [2 ]
Pagh, Rasmus [3 ]
机构
[1] Tech Univ Berlin, Berlin, Germany
[2] NEC Labs Europe, Heidelberg, Germany
[3] IT Univ Copenhagen, Copenhagen, Denmark
[4] Univ Lyon 1, Inria, LBBE, Lyon, France
基金
新加坡国家研究基金会;
关键词
Randomized approximation algorithms; Streaming algorithms; Triangle counting;
D O I
10.1007/s00453-015-0036-4
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
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.
引用
收藏
页码:259 / 278
页数:20
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