1 research outputs found
Optimal strategies for weighted ray search
Searching for a hidden target is an important algorithmic paradigm with
numerous applications. We introduce and study the general setting in which a
number of targets, each with a certain weight, are hidden in a star-like
environment that consists of infinite, concurrent rays, with a common
origin. A mobile searcher, initially located at the origin, explores this
environment in order to locate a set of targets whose aggregate weight is at
least a given value . The cost of the search strategy is defined as the
total distance traversed by the searcher, and its performance is evaluated by
the worst-case ratio of the cost incurred by the searcher over the cost of an
on optimal, offline strategy with (some) access to the instance. This setting
is a broad generalization of well-studied problems in search theory; namely, it
generalizes the setting in which only a single target is sought, as well as the
case in which all targets have unit weights.
We consider two models depending on the amount of information allowed to the
offline algorithm. In the first model, which is the canonical model in search
theory, the offline algorithm has complete information. Here, we propose and
analyze a strategy that attains optimal performance, using a parameterized
approach. In the second model, the offline algorithm has only partial
information on the problem instance (i.e., the target locations). Here, we
present a strategy of asymptotically optimal performance that is
logarithmically related to . This is in stark contrast to the full
information model in which a linear dependency is unavoidable