Wait-Free Approximate Agreement on Graphs

Approximate agreement is one of the few variants of consensus that can be solved in a wait-free manner in asynchronous systems where processes communicate by reading and writing to shared memory. In this work, we consider a natural generalisation of approximate agreement on arbitrary undirected connected graphs. Each process is given a vertex of the graph as input and, if non-faulty, must output a vertex such that all the outputs are within distance 1 of one another, and each output value lies on a shortest path between two input values.