TY - GEN
T1 - "Tri, tri again"
T2 - 26th International Symposium on Distributed Computing, DISC 2012
AU - Dolev, Danny
AU - Lenzen, Christoph
AU - Peled, Shir
PY - 2012
Y1 - 2012
N2 - Let G = (V,E) be an n-vertex graph and M d a d-vertex graph, for some constant d. Is M d 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 O(log n) bits. A simple deterministic algorithm that requires O(n (d-2/d/log n) communication rounds is presented. For the special case that M d is a triangle, we present a probabilistic algorithm that requires an expected O(n 1/3/(t 2/3 + 1)) rounds of communication, where t is the number of triangles in the graph, and 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 O(Δ D+1/n) rounds. For triangles, we devise an algorithm featuring a round complexity of O((A 2 log 2+n/A2 n)/n), where A denotes the arboricity of G.
AB - Let G = (V,E) be an n-vertex graph and M d a d-vertex graph, for some constant d. Is M d 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 O(log n) bits. A simple deterministic algorithm that requires O(n (d-2/d/log n) communication rounds is presented. For the special case that M d is a triangle, we present a probabilistic algorithm that requires an expected O(n 1/3/(t 2/3 + 1)) rounds of communication, where t is the number of triangles in the graph, and 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 O(Δ D+1/n) rounds. For triangles, we devise an algorithm featuring a round complexity of O((A 2 log 2+n/A2 n)/n), where A denotes the arboricity of G.
UR - http://www.scopus.com/inward/record.url?scp=84868368487&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-33651-5_14
DO - 10.1007/978-3-642-33651-5_14
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AN - SCOPUS:84868368487
SN - 9783642336508
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 195
EP - 209
BT - Distributed Computing - 26th International Symposium, DISC 2012, Proceedings
Y2 - 16 October 2012 through 18 October 2012
ER -