Constrained Routing Between Non-Visible Vertices

  • Prosenjit Bose
  • Matias Korman
  • André van RenssenEmail author
  • Sander Verdonschot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10392)


Routing is an important problem in networks. We look at routing in the presence of line segment constraints (i.e., obstacles that our edges are not allowed to cross). Let P be a set of n vertices in the plane and let S be a set of line segments between the vertices in P, with no two line segments intersecting properly. We present the first 1-local O(1)-memory routing algorithm on the visibility graph of P with respect to a set of constraints S (i.e., it never looks beyond the direct neighbours of the current location and does not need to store more than O(1)-information to reach the target). We also show that when routing on any triangulation T of P such that \(S\subseteq T\), no o(n)-competitive routing algorithm exists when only considering the triangles intersected by the line segment from the source to the target (a technique commonly used in the unconstrained setting). Finally, we provide an O(n)-competitive 1-local O(1)-memory routing algorithm on any such T, which is optimal in the worst case, given the lower bound.



We thank Luis Barba, Sangsub Kim, and Maria Saumell for fruitful discussions.


  1. 1.
    Bonichon, N., Gavoille, C., Hanusse, N., Ilcinkas, D.: Connections between theta-graphs, delaunay triangulations, and orthogonal surfaces. In: Thilikos, D.M. (ed.) WG 2010. LNCS, vol. 6410, pp. 266–278. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-16926-7_25 CrossRefGoogle Scholar
  2. 2.
    Bose, P., Fagerberg, R., Renssen, A., Verdonschot, S.: On plane constrained bounded-degree spanners. In: Fernández-Baca, D. (ed.) LATIN 2012. LNCS, vol. 7256, pp. 85–96. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-29344-3_8 CrossRefGoogle Scholar
  3. 3.
    Bose, P., Fagerberg, R., van Renssen, A., Verdonschot, S.: Competitive local routing with constraints. In: Elbassioni, K., Makino, K. (eds.) ISAAC 2015. LNCS, vol. 9472, pp. 23–34. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48971-0_3 CrossRefGoogle Scholar
  4. 4.
    Bose, P., Keil, J.M.: On the stretch factor of the constrained Delaunay triangulation. In: ISVD, pp. 25–31 (2006)Google Scholar
  5. 5.
    Bose, P., Morin, P.: Competitive online routing in geometric graphs. Theor. Comput. Sci. 324(2), 273–288 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bose, P., Morin, P., Stojmenovic, I., Urrutia, J.: Routing with guaranteed delivery in ad hoc wireless networks. Wirel. Netw. 7(6), 609–616 (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    Bose, P., Renssen, A.: Upper bounds on the spanning ratio of constrained theta-graphs. In: Pardo, A., Viola, A. (eds.) LATIN 2014. LNCS, vol. 8392, pp. 108–119. Springer, Heidelberg (2014). doi: 10.1007/978-3-642-54423-1_10 CrossRefGoogle Scholar
  8. 8.
    Clarkson, K.: Approximation algorithms for shortest path motion planning. In: STOC, pp. 56–65 (1987)Google Scholar
  9. 9.
    Das, G.: The visibility graph contains a bounded-degree spanner. In: CCCG, pp. 70–75 (1997)Google Scholar
  10. 10.
    Kranakis, E., Singh, H., Urrutia, J.: Compass routing on geometric networks. In: CCCG, pp. 51–54 (1999)Google Scholar
  11. 11.
    Misra, S., Misra, S.C., Woungang, I.: Guide to Wireless Sensor Networks. Springer, Heidelberg (2009)CrossRefzbMATHGoogle Scholar
  12. 12.
    Räcke, H.: Survey on oblivious routing strategies. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds.) CiE 2009. LNCS, vol. 5635, pp. 419–429. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-03073-4_43 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Matias Korman
    • 2
  • André van Renssen
    • 3
    • 4
    Email author
  • Sander Verdonschot
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Tohoku UniversitySendaiJapan
  3. 3.National Institute of InformaticsTokyoJapan
  4. 4.JST, ERATO, Kawarabayashi Large Graph ProjectTokyoJapan

Personalised recommendations