Abstract
A Searcher wants to find the Home node on a given Network, but his directions are unreliable. At every branch node of a network Q, a Satnav (GPS) points to the arc leading to the destination, or home node, H - but only with a high known probability p. The pointer is fixed in time, so does not change when a node is revisited. Always trusting the Satnav's suggestion may lead to an infinite cycle. If one wishes to reach H in least expected time, with what probability q=q(Q,p) should one trust the pointer (if not, one chooses randomly among the other arcs)? We call this the Faulty Satnav (GPS) Problem. We also consider versions where the trust probability q can depend on the degree of the current node and a ‘treasure hunt’ where two searchers try to reach H first. The agent searching for H need not be a car, that is just a familiar example – it could equally be a UAV receiving unreliable GPS information.This problem has its origin not in driver frustration but in the work of Fonio et al. (2017) [10] on ant navigation, where the pointers correspond to pheromone markers pointing to the nest.
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