Clique counting in graph streams

Abstract

Clique counting is a well studied problem in low memory models like graph streaming. There are algorithms which provide good space complexity bounds for general graphs. For constant pass, approximation algorithms counting triangles or higher order cliques, good lower bounds are known. If we restrict the domain to low-degeneracy graphs, we can devise algorithms parameterized on some sparseness measure (like arbor city) which circumvent this lower bound. One such algorithm for triangle counting is already shown in [1]. In this project, we try to extend that algorithm to counting higher order cliques in such special class of graphs. We give anO(k)-pass, arbitrary order approximation algorithm and analyse its space bounds.