Brief Announcement: Byzantine Geoconsensus

We define and investigate the consensus problem for a set of N processes embedded on the d-dimensional plane, \(d\ge 2\), which we call the geoconsensus problem. The processes have unique coordinates and can communicate with each other through oral messages. In contrast to the literature where processes are individually considered Byzantine, it is considered that all processes covered by a finite-size convex fault area F are Byzantine and there may be one or more processes in a fault area. Similarly as in the literature where correct processes do not know which processes are Byzantine, it is assumed that the fault area location is not known to the correct processes.