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Fast Dispersion of Mobile Robots on Arbitrary Graphs

  • Ajay D. Kshemkalyani
  • Anisur Rahaman Molla
  • Gokarna SharmaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11931)

Abstract

The dispersion problem on graphs asks \(k\le n\) robots placed initially arbitrarily on the nodes of an n-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of the graph. This problem is of significant interest due to its relationship to other fundamental robot coordination problems, such as exploration, scattering, load balancing, and relocation of self-driven electric cars (robots) to recharge stations (nodes). In this paper, we provide a novel deterministic algorithm for dispersion in arbitrary graphs in a synchronous setting where all robots perform their actions in every time step. Our algorithm has \(O(\min (m,k\varDelta ) \cdot \log k)\) steps runtime using \(O(\log n)\) bits of memory at each robot, where m is the number of edges and \(\varDelta \) is the maximum degree of the graph. This is a significant improvement over the O(mk) steps best previously known algorithm that uses logarithmic memory at each robot. In particular, the runtime of our algorithm is optimal (up to a \(O(\log k)\) factor) in constant-degree arbitrary graphs.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ajay D. Kshemkalyani
    • 1
  • Anisur Rahaman Molla
    • 2
  • Gokarna Sharma
    • 3
    Email author
  1. 1.University of Illinois at ChicagoChicagoUSA
  2. 2.Indian Statistical InstituteKolkataIndia
  3. 3.Kent State UniversityKentUSA

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