Approximation Algorithms for Multi-Robot Patrol-Scheduling with Min-Max Latency

Peyman Afshani, Mark de Berg, Kevin Buchin, Jie Gao, Maarten Löffler, Amir Nayyeri, Benjamin Raichel, Rik Sarkar, Haotian Wang, Hao Tsung Yang

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations


We consider the problem of finding patrol schedules for k robots to visit a given set of n sites in a metric space. Each robot has the same maximum speed and the goal is to minimize the weighted maximum latency of any site, where the latency of a site is defined as the maximum time duration between consecutive visits of that site. The problem is NP-hard, as it has the traveling salesman problem as a special case (when k= 1 and all sites have the same weight). We present a polynomial-time algorithm with an approximation factor of O(k2logwmaxwmin) to the optimal solution, where wmax and wmin are the maximum and minimum weight of the sites respectively. Further, we consider the special case where the sites are in 1D. When all sites have the same weight, we present a polynomial-time algorithm to solve the problem exactly. If the sites may have different weights, we present a 12-approximate solution, which runs in time (nwmax/wmin)O(k).

Original languageEnglish
Title of host publicationSpringer Proceedings in Advanced Robotics
PublisherSpringer Science and Business Media B.V.
Number of pages17
StatePublished - 2021

Publication series

NameSpringer Proceedings in Advanced Robotics
ISSN (Print)2511-1256
ISSN (Electronic)2511-1264


  • Approximation
  • Motion planning
  • Scheduling


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