Deterministic subgraph detection in broadcast CONGEST

Abstract

We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: -- For any constant $k$, detecting $k$-paths and trees on $k$ nodes can be done in $O(1)$ rounds. -- For any constant $k$, detecting $k$-cycles and pseudotrees on $k$ nodes can be done in $O(n)$ rounds. -- On $d$-degenerate graphs, cliques and $4$-cycles can be enumerated in $O(d+\log n)$ rounds, and $5$-cycles in $O(d^2+\log n)$ rounds. In many cases, these bounds are tight up to logarithmic factors. Moreover, we show that the algorithms for $d$-degenerate graphs can be improved to optimal complexity $O(d/\log n)$ and $O(d^2/\log n)$, respectively, in the supported CONGEST model, which can be seen as an intermediate model between CONGEST and the congested clique.

References in corpus (5)

• Algebraic Methods in the Congested Clique
• Distributed Subgraph Detection
• Distributed Property Testing for Subgraph-Freeness Revisited
• Fast Distributed Algorithms for Testing Graph Properties
• Distributed Testing of Excluded Subgraphs

Cited by in corpus (6)

• On Distributed Listing of Cliques
• The Communication Complexity of Set Intersection and Multiple Equality Testing
• Brief Announcement: Does Preprocessing Help under Congestion?
• Superlinear Lower Bounds for Distributed Subgraph Detection
• Broadcast Congested Clique: Planted Cliques and Pseudorandom Generators
• On the Power of Preprocessing in Decentralized Network Optimization