A simple local 3-approximation algorithm for vertex cover

Given a graph G = (V , E), a subset of nodes C ⊆ V is a vertex cover if each edge {u, v} ∈ E has u ∈ C or v ∈ C . In this work, we present a constant-time distributed algorithm for finding a factor 3 approximation for minimum vertex cover in bounded-degree graphs. A distributed algorithm that runs in constant time (constant number of synchronous communication rounds) is called a local algorithm [14]. In a local algorithm, the output of a node is a function of the input that is available within its constant-radius neighbourhood; this implies not only high scalability but also high fault-tolerance, making local algorithms desirable for real-world large-scale distributed systems. Unfortunately, to date most results on local algorithms have been negative, even if we use Linial’s [12] model of distributed computing where the message size is unbounded and local computation is free. Linial’s [12] seminal work shows that there is no local algorithm for finding a maximal independent set, maximal matching, or 3colouring of an n-cycle. This holds even if each node is assigned a unique identifier from the set {1,2, . . . ,n}. Ran-