Abstract <p> A line segment (barrier) is specified on the plane, as well as the location of depots. Eachsensor is able to travel a limited-length path, starting and ending at its depot. The part of thebarrier along which the sensor moves is <i>covered</i> by thissensor. It is necessary to place some number of mobile sensors (drones) in each depot in order tocover the entire barrier with a minimum number of drones (<Emphasis FontCategory="NonProportional">MinNum</Emphasis>), or to minimize the total length ofpaths traveled by drones (<Emphasis FontCategory="NonProportional">MinSum</Emphasis>),or to minimize the maximum distance traveled by a drone (<Emphasis FontCategory="NonProportional">MinMax</Emphasis>).</p> <p>Previously, the authors investigated a similar problem with an unlimited numberof drones and, for its solution, proposed a pseudopolynomial algorithm depending on the length ofthe barrier L. In this paper, a generalized problem with a limited number of drones is consideredand, to construct an optimal solution, we propose an algorithm with the same complexity.However, in the case of an unlimited number of drones, the new algorithm has complexity<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L\)</EquationSource> </InlineEquation> times less than the previous one.</p>

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Drone Placement for Optimal Barrier Coverage

  • A. I. Erzin,
  • A. V. Shadrina

摘要

Abstract

A line segment (barrier) is specified on the plane, as well as the location of depots. Eachsensor is able to travel a limited-length path, starting and ending at its depot. The part of thebarrier along which the sensor moves is covered by thissensor. It is necessary to place some number of mobile sensors (drones) in each depot in order tocover the entire barrier with a minimum number of drones (MinNum), or to minimize the total length ofpaths traveled by drones (MinSum),or to minimize the maximum distance traveled by a drone (MinMax).

Previously, the authors investigated a similar problem with an unlimited numberof drones and, for its solution, proposed a pseudopolynomial algorithm depending on the length ofthe barrier L. In this paper, a generalized problem with a limited number of drones is consideredand, to construct an optimal solution, we propose an algorithm with the same complexity.However, in the case of an unlimited number of drones, the new algorithm has complexity \(L\) times less than the previous one.