TY - GEN

T1 - Lower bounds for subgraph detection in the CONGEST model

AU - Gonen, Tzlil

AU - Oshman, Rotem

N1 - Publisher Copyright:
© 2017 Tzlil Gonen and Rotem Oshman.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - In the subgraph-freeness problem, we are given a constant-sized graph H, and wish to determine whether the network graph contains H as a subgraph or not. Until now, the only lower bounds on subgraph-freeness known for the CONGEST model were for cycles of length greater than 3; here we extend and generalize the cycle lower bound, and obtain polynomial lower bounds for subgraph-freeness in the CONGEST model for two classes of subgraphs. The first class contains any graph obtained by starting from a 2-connected graph H for which we already know a lower bound, and replacing the vertices of H by arbitrary connected graphs. We show that the lower bound on H carries over to the new graph. The second class is constructed by starting from a cycle Ck of length k ≥ 4, and constructing a graph H from Ck by replacing each edge {i, (i + 1) mod k} of the cycle with a connected graph Hi, subject to some constraints on the graphs H0, ⋯, Hk-1. In this case we obtain a polynomial lower bound for the new graph H, depending on the size of the shortest cycle in H passing through the vertices of the original k-cycle.

AB - In the subgraph-freeness problem, we are given a constant-sized graph H, and wish to determine whether the network graph contains H as a subgraph or not. Until now, the only lower bounds on subgraph-freeness known for the CONGEST model were for cycles of length greater than 3; here we extend and generalize the cycle lower bound, and obtain polynomial lower bounds for subgraph-freeness in the CONGEST model for two classes of subgraphs. The first class contains any graph obtained by starting from a 2-connected graph H for which we already know a lower bound, and replacing the vertices of H by arbitrary connected graphs. We show that the lower bound on H carries over to the new graph. The second class is constructed by starting from a cycle Ck of length k ≥ 4, and constructing a graph H from Ck by replacing each edge {i, (i + 1) mod k} of the cycle with a connected graph Hi, subject to some constraints on the graphs H0, ⋯, Hk-1. In this case we obtain a polynomial lower bound for the new graph H, depending on the size of the shortest cycle in H passing through the vertices of the original k-cycle.

KW - CONGEST

KW - Lower bounds

KW - Subgraph freeness

UR - http://www.scopus.com/inward/record.url?scp=85045636902&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.OPODIS.2017.6

DO - 10.4230/LIPIcs.OPODIS.2017.6

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AN - SCOPUS:85045636902

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 21st International Conference on Principles of Distributed Systems, OPODIS 2017

A2 - Aspnes, James

A2 - Leitao, Joao

A2 - Bessani, Alysson

A2 - Felber, Pascal

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 21st International Conference on Principles of Distributed Systems, OPODIS 2017

Y2 - 18 December 2017 through 20 December 2017

ER -