Deterministic subgraph detection in broadcast CONGEST

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(d2 + 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(d2/log n), respectively, in the supported CONGEST model, which can be seen as an intermediate model between CONGEST and the congested clique.