Linear Search with Terrain-Dependent Speeds

Abstract

We revisit the linear search problem where a robot, initially placed at the origin on an infinite line, tries to locate a stationary target placed at an unknown position on the line. Unlike previous studies, in which the robot travels along the line at a constant speed, we consider settings where the robot's speed can depend on the direction of travel along the line, or on the profile of the terrain, e.g. when the line is inclined, and the robot can accelerate. Our objective is to design search algorithms that achieve good competitive ratios for the time spent by the robot to complete its search versus the time spent by an omniscient robot that knows the location of the target.We consider several new robot mobility models in which the speed of the robot depends on the terrain. These include 1) different constant speeds for different directions, 2) speed with constant acceleration and/or variability depending on whether a certain segment has already been searched, 3) speed dependent on the incline of the terrain. We provide both upper and lower bounds on the competitive ratios of search algorithms for these models, and in many cases, we derive optimal algorithms for the search time.

Distributed Systems and Mobile Computing

“…Since the inception of 2 EVAC F2F in [1], numerous search and evacuation-type variants have emerged that studied different robot specs and/or number of searchers, different communication models, and different domains. Some notable examples include search and/or evacuation in the disk with more than 1 exits [29,30], in triangles [31,32], on multiple rays [33], in graphs [34,35], on a line with at least two robots [36,37] (generalizing the seminal result of [38]), with faulty robots [39][40][41] or with probabilistically faulty robots [42], with advice (information) [43], with priority specification on the searchers [44,45], with immobile agents [46,47], with time/energy trade-off requirements [48,49], with speed bounds [50], and with terrain dependent speeds [51], just to name some. The interested reader may also see the recent survey [52] that elaborates more on some selected topics.…”

Evacuating from ell_p Unit Disks in the Wireless Model

“…Search and evacuation problems with faulty robots have been studied in [22,38,49] and with probabilistically faulty robots in [13]. Variations pertaining to the searcher's speeds appeared in [36,37] (immobile agents), in [44] (speed bounds) and in [26] (terrain dependent speeds). Search for multiple exits was considered in [28,50], while variation of searching with advice appeared in [40].…”

A Multi-Objective Optimization Problem on Evacuating 2 Robots from the Disk in the Face-to-Face Model; Trade-Offs between Worst-Case and Average-Case Analysis

“…Since the inception of 2 EVAC F2F in [1], numerous search and evacuation-type variants have emerged that studied different robot specs and/or number of searchers, different communication models, and different domains. Some notable examples include search and/or evacuation in the disk with more than 1 exits [29,30], in triangles [31,32], on multiple rays [33], in graphs [34,35], on a line with at least two robots [36,37] (generalizing the seminal result of [38]), with faulty robots [39][40][41] or with probabilistically faulty robots [42], with advice (information) [43], with priority specification on the searchers [44,45], with immobile agents [46,47], with time/energy trade-off requirements [48,49], with speed bounds [50], and with terrain dependent speeds [51], just to name some. The interested reader may also see the recent survey [52] that elaborates more on some selected topics.…”