How information prospection facilitates spatial coverage of self-avoiding walks

Abstract

Information gathering and processing can be particularly useful to enhance the efficiency of living organisms when searching or foraging under uncertain scenarios. Assuming that such situations can be conveniently modeled through random walk models, a case that has been widely explored in the physical literature is the generation of self-avoiding trajectories as a mechanism to increase the area of the region explored and so the search efficiency. Additionally, other mechanisms as the ability to prospect the possible outcomes from choosing between different paths/trajectories could potentially enhance such efficiency even further. Here we use an extension of the classical true self-avoiding random walk model to explore that idea. We evaluate numerically how the coverage time of such random walk model gets modified when a basic prospection mechanism, which allows the walker to anticipate the outcome of possible future paths, is introduced. We analyze the level of prospection that is required to optimize the mean coverage time in a regular domain and report two relevant findings. First, we observe that increasing more and more the information used for prospection is just optimal provided the organism can process it adequately (which occurs when the self-avoidance mechanism is reliable enough), but it can be even detrimental when self-avoidance (i.e. memory) is poor or impaired. Second, we surprisingly find that prospection carried out at different time scales can be as optimal as one based on a fixed large prospection time scale. We claim that such results may capture some basic traits from the real strategies used by higher organisms when searching under uncertainty.