Advertisement

Constrained shortest path problems in bi-colored graphs: a label-setting approach

  • Amin AliAbdi
  • Ali MohadesEmail author
  • Mansoor Davoodi
Article
  • 6 Downloads

Abstract

Definition of an optimal path in the real-world routing problems is not necessarily the shortest one, because parameters such as travel time, safety, quality, and smoothness also played essential roles in the definition of optimality. In this paper, we use bi-colored graphs for modeling urban and heterogeneous environments and introduce variations of constraint routing problems. Bi-colored graphs are a kind of directed graphs whose vertices are divided into two subsets of white and gray. We consider two criteria, minimizing the length and minimizing the number of gray vertices and present two problems called gray vertices bounded shortest path problem and length bounded shortest path problem on bi-colored graphs. We propose an efficient time label-setting algorithm to solve these problems. Likewise, we simulate the algorithm and compare it with the related path planning methods on random graphs as well as real-world environments. The simulation results show the efficiency of the proposed algorithm.

Keywords

Constraint shortest path Bi-colored graphs Transportation Urban routing problem Road networks 

Notes

References

  1. 1.
    LaValle SM (2006) Planning algorithms. Cambridge University Press, CambridgeGoogle Scholar
  2. 2.
    Turner L, Hamacher HW (2011) On Universal Shortest Paths. Springer Berlin Heidelberg, pp 313–318Google Scholar
  3. 3.
    Gourvès L, Lyra A, Martinhon C, Monnot J, Protti F (2009) On s-t paths and trails in edge-colored graphs. Electronic Notes in Discrete Mathematics 35:221–226.  https://doi.org/10.1016/j.endm.2009.11.037 CrossRefGoogle Scholar
  4. 4.
    Garey MR, Johnson DS (1979) Computers and intracability: A guide to the theory of NP-completeness. W.H. Freeman, New York, NY, USAGoogle Scholar
  5. 5.
    Silva R, Craveirinha J (2004) An Overview of routing models for MPLS Networks. In: 1st Workshop Multicriteria Modelling in Telecommunication Network Planning and Design. Faculty of Economics of the University of Coimbra, Coimbra, Portugal, pp 17–24Google Scholar
  6. 6.
    Festa P (2015) Constrained shortest path problems: state-of-the-art and recent advances. In: 2015 17th International Conference on Transparent Optical Networks (ICTON). IEEE, pp 1–17Google Scholar
  7. 7.
    Davoodi M (2017) Bi-objective path planning using deterministic algorithms. Robotics and Autonomous Systems 93:105–115.  https://doi.org/10.1016/j.robot.2017.03.021 CrossRefGoogle Scholar
  8. 8.
    Davoodi M, Panahi F, Mohades A, Hashemi SN (2013) Multi-objective path planning in discrete space. Applied Soft Computing 13:709–720.  https://doi.org/10.1016/J.ASOC.2012.07.023 CrossRefGoogle Scholar
  9. 9.
    Jaffe JM (1984) Algorithms for finding paths with multiple constraints. Networks 14:95–116.  https://doi.org/10.1002/net.3230140109 CrossRefGoogle Scholar
  10. 10.
    Lorenz DH, Raz D (2001) A simple efficient approximation scheme for the restricted shortest path problem. Operations Research Letters 28:213–219.  https://doi.org/10.1016/S0167-6377(01)00069-4 CrossRefGoogle Scholar
  11. 11.
    Hassin R (1992) Approximation Schemes for the Restricted Shortest Path Problem. Math Oper Res 17:36–42.  https://doi.org/10.1287/moor.17.1.36 CrossRefGoogle Scholar
  12. 12.
    Dumitrescu I, Boland N (2001) Algorithms for the Weight Constrained Shortest Path Problem. International Transactions in Operational Research 8:15–29.  https://doi.org/10.1111/1475-3995.00003 CrossRefGoogle Scholar
  13. 13.
    Dumitrescu I, Boland N (2003) Improved Preprocessing, Labeling and Scaling Algorithms for the Weight-Constrained Shortest Path Problem. Networks 42:135–153.  https://doi.org/10.1002/net.10090 CrossRefGoogle Scholar
  14. 14.
    Chen S, Song M, Sahni S (2008) Two techniques for fast computation of constrained shortest paths. IEEE/ACM Transactions on Networking 16:105–115.  https://doi.org/10.1109/TNET.2007.897965 CrossRefGoogle Scholar
  15. 15.
    Santos L, Coutinho-Rodrigues J, Current JR (2007) An improved solution algorithm for the constrained shortest path problem. Transportation Research Part B: Methodological 41:756–771.  https://doi.org/10.1016/j.trb.2006.12.001 CrossRefGoogle Scholar
  16. 16.
    Ergun F, Sinha R, Zhang L (2002) An improved FPTAS for Restricted Shortest Path. Information Processing Letters 83:287–291.  https://doi.org/10.1016/S0020-0190(02)00205-3 CrossRefGoogle Scholar
  17. 17.
    Chen G, Xue G (2003) A PTAS for weight constrained Steiner trees in series–parallel graphs. Theoretical Computer Science 304:237–247.  https://doi.org/10.1016/S0304-3975(03)00088-4 CrossRefGoogle Scholar
  18. 18.
    Xin Yuan, Xingming Liu (2001) Heuristic algorithms for multi-constrained quality of service routing. In: Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213). IEEE, pp 844–853Google Scholar
  19. 19.
    Zheng Wang, Crowcroft J (1996) Quality-of-service routing for supporting multimedia applications. IEEE Journal on Selected Areas in Communications 14:1228–1234.  https://doi.org/10.1109/49.536364 CrossRefGoogle Scholar
  20. 20.
    Tarapata Z (2007) Selected Multicriteria Shortest Path Problems: An Analysis of Complexity, Models and Adaptation of Standard Algorithms. International Journal of Applied Mathematics and Computer Science 17:269–287.  https://doi.org/10.2478/v10006-007-0023-2 CrossRefGoogle Scholar
  21. 21.
    Yen JY (1971) Finding the K shortest loopless paths in a network. Management Science 17:712–716.  https://doi.org/10.1287/mnsc.17.11.712 CrossRefGoogle Scholar
  22. 22.
    Eppstein D (1998) Finding the k Shortest Paths. SIAM Journal on Computing 28:652–673.  https://doi.org/10.1137/S0097539795290477 CrossRefGoogle Scholar
  23. 23.
    Akiba T, Hayashi T, Nori N, Iwata Y, Yoshida Y (2015) Efficient Top-k Shortest-path Distance Queries on Large Networks by Pruned Landmark Labeling. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence. AAAI Press, pp 2–8Google Scholar
  24. 24.
    Burstein D, Metcalf L (2016) The K Shortest Paths Problem with Application to Routing. 1–37Google Scholar
  25. 25.
    Zhang S, Liu X (2013) A new algorithm for finding the k shortest transport paths in dynamic stochastic networks. Journal of Vibroengineering 15:726–735Google Scholar
  26. 26.
    Scano G, Huguet MJ, Ngueveu SU (2016) Adaptations of k-shortest path algorithms for transportation networks. In: Proceedings of 2015 International Conference on Industrial Engineering and Systems Management, IEEE IESM 2015. pp 663–669Google Scholar
  27. 27.
    Guo J, Jia L (2017) A new algorithm for finding the K shortest paths in a time-schedule network with constraints on arcs. Journal of Algorithms and Computational Technology 11:170–177.  https://doi.org/10.1177/1748301816680470 CrossRefGoogle Scholar
  28. 28.
    Chondrogiannis T, Bouros P, Gamper J, Leser U (2017) Exact and Approximate Algorithms for Finding k-Shortest Paths with Limited Overlap. In: 20th International Conference on Extending Database Technology : EDBT 2017. pp 414–425Google Scholar
  29. 29.
    Wang S, Yang Y, Hu X, Li J, Xu B (2016) Solving the K -shortest paths problem in timetable-based public transportation systems. Journal of Intelligent Transportation Systems 20:413–427.  https://doi.org/10.1080/15472450.2015.1082911 CrossRefGoogle Scholar
  30. 30.
    Eppstein D (1994) Finding the k shortest paths. In: 35th Annual Symposium on Foundations of Computer Science. IEEE, pp 154–165Google Scholar
  31. 31.
    Eppstein D, Gupta S (2017) Crossing Patterns in Nonplanar Road Networks. In: Proceedings of the 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - SIGSPATIAL’17. ACM Press, New York, New York, USA, pp 1–9Google Scholar
  32. 32.
    Masucci AP, Smith D, Crooks A, Batty M (2009) Random planar graphs and the London street network. The European Physical Journal B 71:259–271.  https://doi.org/10.1140/epjb/e2009-00290-4 CrossRefGoogle Scholar
  33. 33.
    Schultes D (2008) Route Planning in Road Networks. VDM VerlagGoogle Scholar
  34. 34.
    Zhang Y, Liu J, Qian X, Qiu A, Zhang F (2017) An Automatic Road Network Construction Method Using Massive GPS Trajectory Data. ISPRS International Journal of Geo-Information 6:400.  https://doi.org/10.3390/ijgi6120400 CrossRefGoogle Scholar
  35. 35.
    Wang X, You S, Wang L (2017) Classifying road network patterns using multinomial logit model. Journal of Transport Geography 58:104–112.  https://doi.org/10.1016/j.jtrangeo.2016.11.013 CrossRefGoogle Scholar
  36. 36.
    Gupta S (2018) Topological Algorithms for Geographic and Geometric Graphs. University Of California, Irvine TopologicalGoogle Scholar
  37. 37.
    Yang B, Guo C, Ma Y, Jensen CS (2015) Toward personalized, context-aware routing. The VLDB Journal 24:297–318.  https://doi.org/10.1007/s00778-015-0378-1 CrossRefGoogle Scholar
  38. 38.
    Ceikute V, Jensen CS (2013) Routing Service Quality -- Local Driver Behavior Versus Routing Services. In: 2013 IEEE 14th International Conference on Mobile Data Management. IEEE, pp 97–106Google Scholar
  39. 39.
    Funke S, Storandt S (2015) Personalized route planning in road networks. In: Proceedings of the 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems - GIS ’15. ACM Press, New York, New York, USA, pp 1–10Google Scholar
  40. 40.
    Delling D, Wagner D (2009) Time-dependent route planning. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer, Berlin, Heidelberg, pp 207–230CrossRefGoogle Scholar
  41. 41.
    ter Mors AW, Witteveen C, Zutt J, Kuipers FA (2010) Context-Aware Route Planning. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer, Berlin, Heidelberg, pp 138–149CrossRefGoogle Scholar
  42. 42.
    Li PH, Yiu ML, Mouratidis K (2017) Discovering historic traffic-tolerant paths in road networks. GeoInformatica 21:1–32.  https://doi.org/10.1007/s10707-016-0265-y CrossRefGoogle Scholar
  43. 43.
    Geisberger R, Sanders P, Schultes D, Delling D (2008) Contraction hierarchies: Faster and simpler hierarchical routing in road networks. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Berlin Heidelberg, Berlin, Heidelberg, pp 319–333Google Scholar
  44. 44.
    Bast H, Delling D, Goldberg A, Müller-Hannemann M, Pajor T, Sanders P, Wagner D, Werneck RF (2016) Route Planning in Transportation Networks. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). pp 19–80CrossRefGoogle Scholar
  45. 45.
    Ahmadi MH, Haghighatdoost V (2017) General Time-Dependent Sequenced Route Queries in Road Networks. In: 2017 IEEE 15th Intl Conf on Dependable, Autonomic and Secure Computing, 15th Intl Conf on Pervasive Intelligence and Computing, 3rd Intl Conf on Big Data Intelligence and Computing and Cyber Science and Technology Congress(DASC/PiCom/DataCom/CyberSciTech). IEEE, New York, New York, USA, pp 949–956Google Scholar
  46. 46.
    Dibbelt J, Strasser B, Wagner D (2015) Fast exact shortest path and distance queries on road networks with parametrized costs. In: Proceedings of the 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems - GIS ’15. ACM Press, New York, New York, USA, pp 1–4Google Scholar
  47. 47.
    Delling D, Goldberg A V, Pajor T, Werneck RF (2017) Customizable Route Planning in Road Networks. Transportation Science 51:566–591.  https://doi.org/10.1287/trsc.2014.0579 CrossRefGoogle Scholar
  48. 48.
    Yu J, Zhang Z, Sarwat M (2018) Spatial data management in apache spark: the GeoSpark perspective and beyond. GeoInformatica.  https://doi.org/10.1007/s10707-018-0330-9 CrossRefGoogle Scholar
  49. 49.
    Eldawy A (2016) SpatialHadoop: A MapReduce Framework for Big Spatial DataGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratory of Algorithms and Computational Geometry, Department of Mathematics and Computer ScienceAmirkabir University of Technology (Tehran Polytechnic)TehranIran
  2. 2.Department of Computer Science and Information TechnologyInstitute for Advanced Studies in Basic Sciences (IASBS)ZanjanIran

Personalised recommendations