Overcoming Probabilistic Faults in Disoriented Linear Search

We consider search by mobile agents for a hidden, idle target, placed on the infinite line. Feasible solutions are agent trajectories in which all reach target sooner or later. A special feature of our problem is that p-faulty, meaning every attempt to change direction an independent Bernoulli trial with known probability p, where p turn fails. looking minimize worst-case expected termination time, relative distance hidden origin (competitive analysis). Hence, searching one 0-faulty celebrated linear (cow-path) admits optimal 9 and 4.59112 competitive ratios, deterministic randomized algorithms, respectively. First, we study p-faulty agent, i.e., no access random oracles, $$p\in (0,1/2)$$ . For this problem, provide leverage probabilistic faults into algorithmic advantage. Our strongest result pertains algorithm (deterministic, aside from adversarial faults) which, as $$p\rightarrow 0$$ , has performance $$4.59112+\epsilon $$ up additive term $$\epsilon can be arbitrarily small. Additionally, it less than $$p\le 0.390388$$ When 1/2$$ $$\Theta (1/(1-2p))$$ also show constant factor. Second, two agents, three algorithms different advantages, bounded ratio even Indeed, how simulate trajectory any (deterministic randomized), independently underlying communication model. As result, allows solution $$9+\epsilon (which achieved high concentration) final contribution novel achieves $$3+4\sqrt{p(1-p)}$$ concentration.