Linear Search with Terrain-Dependent Speeds

  • Jurek Czyzowicz
  • Evangelos Kranakis
  • Danny Krizanc
  • Lata Narayanan
  • Jaroslav Opatrny
  • Sunil Shende
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10236)


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.


Search algorithm Zig-zag algorithm Competitive ratio Linear terrain Robot Speed of movement 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jurek Czyzowicz
    • 1
  • Evangelos Kranakis
    • 2
  • Danny Krizanc
    • 3
  • Lata Narayanan
    • 4
  • Jaroslav Opatrny
    • 4
  • Sunil Shende
    • 5
  1. 1.Dép. d’informatiqueUniversité du Québec en OutaouaisGatineauCanada
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada
  3. 3.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA
  4. 4.Department of Computer Science and Software EngineeringConcordia UniversityMontrealCanada
  5. 5.Department of Computer ScienceRutgers UniversityCamdenUSA

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