Arboricity and subgraph listing algorithms
SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Testing subgraphs in large graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
MST construction in O(log log n) communication rounds
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Testing Triangle-Freeness in General Graphs
SIAM Journal on Discrete Mathematics
Distributed coloring in Õ (√log n) Bit Rounds
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Tight bounds for parallel randomized load balancing: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
Distributed verification and hardness of distributed approximation
Proceedings of the forty-third annual ACM symposium on Theory of computing
The round complexity of distributed sorting: extended abstract
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
"Tri, tri again": finding triangles and small subgraphs in a distributed setting
DISC'12 Proceedings of the 26th international conference on Distributed Computing
"Tri, tri again": finding triangles and small subgraphs in a distributed setting
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Optimal deterministic routing and sorting on the congested clique
Proceedings of the 2013 ACM symposium on Principles of distributed computing
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Let G=(V,E) be an n-vertex graph and Md a d-vertex graph, for some constant d. Is Md a subgraph of G? We consider this problem in a model where all n processes are connected to all other processes, and each message contains up to $\mathcal{O}(\log n)$ bits. A simple deterministic algorithm that requires $\mathcal{O}(n^{(d-2)/d}/\log n)$ communication rounds is presented. For the special case that Md is a triangle, we present a probabilistic algorithm that requires an expected $\mathcal{O}(n^{1/3}/(t^ {2/3}+1))$ rounds of communication, where t is the number of triangles in the graph, and $\mathcal{O}(\min\{n^{1/3}\log^{2/3}n/(t^ {2/3}+1),n^{1/3}\})$ with high probability. We also present deterministic algorithms that are specially suited for sparse graphs. In graphs of maximum degree Δ, we can test for arbitrary subgraphs of diameter D in $\mathcal{O}(\Delta^{D+1}/n)$ rounds. For triangles, we devise an algorithm featuring a round complexity of $\mathcal{O}((A^2\log_{2+n/A^2} n)/n)$, where A denotes the arboricity of G.