  Autonomous robots are commonly tasked with the problem of area exploration
and search for certain targets or artifacts of interest to be tracked.
Traditionally, the problem formulation considered is that of complete search
and thus - ideally - identification of all targets of interest. An important
problem however which is not often addressed is that of time-efficient
memoryless search under sparse rewards that may be worth visited any number of
items. In this paper we specifically address the largely understudied problem
of optimizing the "time-of-arrival" or "time-of-detection" to robotically
search for sparsely distributed rewards (detect targets of interest) within
large-scale environments and subject to memoryless exploration. At the core of
the proposed solution is the fact that a search-based L\'evy walk consisting of
a constant velocity search following a L\'evy flight path is optimal for
searching sparse and randomly distributed target regions in the lack of map
memory. A set of results accompany the presentation of the method, demonstrate
its properties and justify the purpose of its use towards large-scale area
exploration autonomy.
