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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.
We study the maximum cardinality matching problem in a standard distributed setting, where the nodes $V$ of a given $n$-node network graph $G=(V,E)$ communicate over the edges $E$ in synchronous rounds. More specifically, we consider the distributed
We give efficient randomized and deterministic distributed algorithms for computing a distance-$2$ vertex coloring of a graph $G$ in the CONGEST model. In particular, if $Delta$ is the maximum degree of $G$, we show that there is a randomized CONGEST
Energy is often the most constrained resource in networks of battery-powered devices, and as devices become smaller, they spend a larger fraction of their energy on communication (transceiver usage) not computation. As an imperfect proxy for true ene
Broadcast is one of the fundamental network communication primitives. One node of a network, called the $mathit{source}$, has a message that has to be learned by all other nodes. We consider the feasibility of deterministic broadcast in radio network
In this paper, we consider the Byzantine reliable broadcast problem on authenticated and partially connected networks. The state-of-the-art method to solve this problem consists in combining two algorithms from the literature. Handling asynchrony and