Abstract
In this paper we demonstrate the application of time-varying graphs (TVGs) for modeling and analyzing multi-robot foremost coverage in dynamic environments. In particular, we consider the multi-robot, multi-depot Dynamic Map Visitation Problem (DMVP), in which a team of robots must visit a collection of critical locations as quickly as possible, in an environment that may change rapidly and unpredictably during navigation. We analyze DMVP in the context of the \(\mathcal {R} \supset \mathcal {B} \supset \mathcal {P}\) TVG hierarchy. We present exact offline algorithms for \(k\) robots on edge-recurrent TVGs (\(\mathcal {R}\)) over a range of topologies motivated by border coverage: an \(O(Tn)\) algorithm on a path and an \(O(T\frac{n^2}{k})\) algorithm on a cycle (where \(T\) is a time bound that is linear in the input size), as well as polynomial and fixed parameter tractable solutions for more general notions of border coverage. We also present algorithms for the case of two robots on a tree (and outline generalizations to \(k\) robots), including an \(O(n^5)\) exact algorithm for the case of edge-periodic TVGs (\(\mathcal {P}\)) with period 2, and a tight poly-time approximation for time-bounded edge-recurrent TVGs (\(\mathcal {B}\)). Finally, we present a linear-time \(\frac{12 \varDelta }{5}\)-approximation for two robots on general graphs in \(\mathcal {B}\) with edge-recurrence bound \(\varDelta \).
Keywords
- Time-varying Graphs (TVG)
- Border Coverage
- fixed-parameter Tractable (FPT)
- Spanning Tree Coverage
- Topological Length
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aaron, E., Kranakis, E., Krizanc, D.: On the complexity of the multi-robot, multi-depot map visitation problem. In: IEEE MASS, pp. 795–800 (2011)
Aaron, E., Krizanc, D., Meyerson, E.: DMVP: Foremost waypoint coverage of time-varying graphs. In: Kratsch, D., Todinca, I. (eds.) WG 2014. LNCS, vol. 8747, pp. 29–41. Springer, Heidelberg (2014). http://www.univ-orleans.fr/lifo/evenements/WG2014/
Baumann, H., Crescenzi, P., Fraigniaud, P.: Parsimonious flooding in dynamic graphs. Distr. Comp. 24(1), 31–44 (2011)
Bektas, T.: The multiple traveling salesman problem: an overview of formulations and solution procedures. OMEGA 34(3), 209–219 (2006)
Bhadra, S., Ferreira, A.: Complexity of connected components in evolving graphs and the computation of multicast trees in dynamic networks. In: Pierre, S., Barbeau, M., An, H.-C. (eds.) ADHOC-NOW 2003. LNCS, vol. 2865, pp. 259–270. Springer, Heidelberg (2003)
Bui-Xuan, B., Ferreira, A., Jarry, A.: Computing shortest, fastest, and foremost journeys in dynamic networks. IJ Found. Comp. Sci. 14(02), 267–285 (2003)
Casteigts, A., Flocchini, P., Mans, B., Santoro, N.: Deterministic computations in time-varying graphs: broadcasting under unstructured mobility. In: Calude, C.S., Sassone, V. (eds.) TCS 2010. IFIP AICT, vol. 323, pp. 111–124. Springer, Heidelberg (2010)
Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. IJPED 27(5), 387–408 (2012)
Avin, C., Koucký, M., Lotker, Z.: How to explore a fast-changing world (Cover Time of a Simple Random Walk on Evolving Graphs). In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 121–132. Springer, Heidelberg (2008)
Choset, H.: Coverage for robotics - a survey of recent results. Ann. Math. Artif. Intell. 31, 113–126 (2001)
Correll, N., Rutishauser, S., Martinoli, A.: Comparing coordination schemes for miniature robotic swarms: a case study in boundary coverage of regular structures. In: Khatib, O., Kumar, V., Rus, D. (eds.) Experimental Robotics. STAR, vol. 39, pp. 471–480. Springer, Heidelberg (2008)
Dynia, M., Korzeniowski, M., Schindelhauer, C.: Power-aware collective tree exploration. In: Grass, W., Sick, B., Waldschmidt, K. (eds.) ARCS 2006. LNCS, vol. 3894, pp. 341–351. Springer, Heidelberg (2006)
Dynia, M., Kutyłowski, J., der Heide, F.M., Schindelhauer, C.: Smart robot teams exploring sparse trees. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 327–338. Springer, Heidelberg (2006)
Easton, K., Burdick, J.: A coverage algorithm for multi-robot boundary inspection. In: Proceedings of ICRA, pp. 727–734 (2005)
Fakcharoenphol, J., Harrelson, C., Rao, S.: The \(k\)-traveling repairman problem. ACM Trans. Algorithms 3(4) (2007). http://dl.acm.org/citation.cfm?doid=1290672.1290677
Flocchini, P., Mans, B., Santoro, N.: On the exploration of time-varying networks. Theor. Comput. Sci. 469, 53–68 (2013)
Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
Godard, E., Mazauric D.: Computing the dynamic diameter of non-deterministic dynamic networks is hard. In: Gao, J., Efrat, A., Fekete, S.P., Zhang, Y. (eds.) ALGOSENSORS 2014. LNCS, vol. 8847, pp. 88–102. Springer, Heidelberg (2015)
Ilcinkas, D., Wade, A.M.: On the power of waiting when exploring public transportation systems. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 451–464. Springer, Heidelberg (2011)
Ilcinkas, D., Wade, A.M.: Exploration of the T-Interval-Connected Dynamic Graphs: the case of the ring. In: Moscibroda, T., Rescigno, A.A. (eds.) SIROCCO 2013. LNCS, vol. 8179, pp. 13–23. Springer, Heidelberg (2013)
Kuhn, F., Lynch, N., Oshman, R.: Distributed computation in dynamic networks. In: STOC, pp. 513–522 (2010)
Kuhn, F., Oshman, R.: Dynamic networks: models and algorithms. ACM SIGACT News 42(1), 82–96 (2011)
Kumar, S., Lai, T., Arora, A.: Barrier coverage with wireless sensors. In: ACM MobiCom, pp. 284–298 (2005)
Mans, B., Mathieson, L.: On the treewidth of dynamic graphs. In: Du, D.-Z., Zhang, G. (eds.) COCOON 2013. LNCS, vol. 7936, pp. 349–360. Springer, Heidelberg (2013)
Michail, O., Spirakis, P.G.: Traveling salesman problems in temporal graphs. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds.) MFCS 2014, Part II. LNCS, vol. 8635, pp. 553–564. Springer, Heidelberg (2014)
Nagamochi, H., Okada, K.: A faster 2-approximation algorithm for the minmax p-traveling salesmen problem on a tree. Discrete Applied Math. 140(1-3), 103–114 (2004)
Xu, L., Xu, Z., Xu, D.: Exact and approximation algorithms for the minmax k-traveling salesmen problem on a tree. EJOR 227, 284–292 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aaron, E., Krizanc, D., Meyerson, E. (2015). Multi-Robot Foremost Coverage of Time-Varying Graphs. In: Gao, J., Efrat, A., Fekete, S., Zhang, Y. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2014. Lecture Notes in Computer Science(), vol 8847. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46018-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-46018-4_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-46017-7
Online ISBN: 978-3-662-46018-4
eBook Packages: Computer ScienceComputer Science (R0)