Search and Rescue on the Line

Abstract

We propose and study a problem inspired by a common task in disaster, military, and other emergency scenarios: search and rescue. Suppose an object (victim, message, target, etc.) is at some unknown location on a path. Given one or more mobile agents, also at initially arbitrary locations on the path, the goal is to find and deliver the object to a predefined destination in as little time as possible. We study the problem for the one- and two-agent cases and consider scenarios where the object and agents are arbitrarily (adversarially, even) placed along a path of either known (and finite) or unknown (and potentially infinite) length. We also consider scenarios where the destination is either at the endpoint or in the middle of the path. We provide both deterministic and randomized online algorithms for each of these scenarios and prove bounds on their (expected) competitive ratios.