This Article 
 Bibliographic References 
 Add to: 
Multihierarchical Graph Search
January 2002 (vol. 24 no. 1)
pp. 103-113

The use of hierarchical graph search for finding paths in graphs is well known in the literature, providing better results than plain graph search regarding computational costs in many cases. This paper offers a step forward by including multiple hierarchies in a graph-based model. Such a multihierarchical model has the following advantages: First, a multiple hierarchy permits us to choose the best hierarchy to solve each search problem; second, when several search problems have to be solved, a multiple hierarchy provides the possibility of solving part of them simultaneously; and third, solutions to the search problems can be expressed in any of the hierarchies of the multiple hierarchy, which allows us to represent the information in the most suitable way for each specific purpose. In general, multiple hierarchies have proven to be a more adaptable model than single-hierarchy or nonhierarchical models. This paper formalizes the multihierarchical model, describes the techniques that have been designed for taking advantage of multiple hierarchies in a hierarchical path search, and presents some experiments and results on the performance of these techniques.

[1] R.A. Brooks, “Solving the Find-Path Problem by Good Representation of Free Space,” Autonomous Robot Vehicles, J. Cox and G.T. Wilfong, eds., pp. 290-297, 1990.
[2] A. Bundy, F. Giunchiglia, and T. Walsh, “Building Abstractions,” Proc. AAAI-90 Workshop Automatic Generation of Approximations and Abstraction, pp. 221-232, 1990.
[3] A. Car and A.U. Frank, “Modeling a Hierarchy of Space Applied to Large Road Networks,” Lecture Notes in Computer Science, J. Nievergelt et al., eds., vol. 884, pp. 15-24, 1994.
[4] M. Dario and S. Rizzi, “Dynamic Clustering of Maps in Autonomous Agents,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 11, pp. 1080-1091, 1996.
[5] E.W. Dijkstra, “A Note on Two Problems in Connection with Graphs,” Numerische Mathematik, vol. 1, pp. 269-271, 1959.
[6] C. Fennema, A. Hanson, E. Riseman, J.R. Beveridge, and R. Kumar, "Model-Directed Mobile Robot Navigation," IEEE Trans. Systems, Man, and Cybernetics, vol. 20, no. 6, pp. 1,352-1,369, Nov./Dec. 1990.
[7] J.A. Fernández, “Modeling and Generation of Multiple Abstractions for Representing Large-Scale Space: An Application to Mobile Robots,” PhD thesis, Dept. of System Eng. and Automation, Univ. of Málaga, Spain, 2000.
[8] J.A. Fernández, J. González, L. Mandow, and J.L. Pérez-de-la-Cruz, “Mobile Robot Path Planning: A Multicriteria Approach,” Eng. Applications of Artificial Intelligence, vol. 12, no. 4, pp. 543-554, 1999.
[9] J.A. Fernández and J. González, “A General World Representation for Mobile Robot Operations,” Proc. Seventh Conf. Spanish Assoc. Artificial Intelligence (CAEPIA '97), pp. 35-44, 1997.
[10] J.A. Fernández and J. González, “Hierarchical Path Search for Mobile Robot Path Planning,” Proc. IEEE Int'l Conf. Robotics and Automation (ICRA '98), 1998.
[11] R.W. Floyd, “Algorithm 97: Shortest Path,” Comm. ACM, vol. 5, no. 6, pp. 345, 1962.
[12] K. Fujimura, “Time-Minimum Routes in Time-Dependent Networks,” IEEE Trans. Robotics and Automation, vol. 11, no. 3, pp. 343-351, 1995.
[13] E. Giunchiglia and T. Walsh, “Using Abstraction,” Technical Report #9010-08, Instituto per la Ricerca Scientifica e Tecnologica, Italy, 1990.
[14] P.E. Hart, N.J. Nilsson, and B. Raphael, “A Formal Basis for the Heuristic Determination of Minimum Cost Paths,” IEEE Trans. Systems, Man, and Cybernetics, vol. 4, no. 2, 1968.
[15] R.C. Holte, C. Drummond, M.B. Pérez, R.M. Zimmer, and A.J. MacDonald, “Searching with Abstractions: A Unifying Framework and New High-Performance Algorithm,” Proc. 10th Canadian Conf. Artificial Intelligence (AI '94), pp. 263-270, 1994.
[16] R.C. Holte, M.B. Pérez, R.M. Zimmer, and A.J. MacDonald, “The Tradeoff Between Speed and Optimality in Hierarchical Search,” Technical Report TR-95-19, Univ. of Ottawa, Canada, 1995.
[17] P.D. Holmes and E.R. Jungert, “Symbolic and Geometric Connectivity Graph Methods for Route Planning in Digitized Maps,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 5, pp. 549-565, 1992.
[18] H. Hu and M. Brady, “Dynamic Global Path Planning with Uncertainty for Mobile Robots in Manufacturing,” IEEE Trans. Robotics and Automation, vol. 13, no. 5, pp. 760-767, 1997.
[19] N. Jing, Y. Huang, and E. Rundensteiner, “Hierarchical Optimization of Optimal Path Finding for Transportation Applications,” Proc. Fifth Int'l Conf. Information and Knowledge Management, pp. 261-268, 1996.
[20] R.E. Korf, “Planning as Search: A Quantitative Approach,” Artificial Intelligence, vol. 33, pp. 65-88, 1987.
[21] B.J. Kuipers, “A Hierarchy of Qualitative Representations of Space,” Proc. Working Papers 10th Int'l Workshop Qualitative Reasoning (QR '96), 1996.
[22] A. Ollero, A. Simon, F. García, and V.E. Torres, “Integrated Mechanical Design of a New Mobile Robot,” Proc. Int'l Federation of Automatic Control Symp., 1992.
[23] I.P. Park and J.R. Kender, “Topological Direction-Giving and Visual Navigation in Large Environments,” Artificial Intelligence, vol. 78, 1995.
[24] E. Remolina, J.A. Fernández, B.J. Kuipers, and J. González, “Formalizing Regions in the Spatial Semantic Hierarchy: An AH-graphs Implementation Approach,” Spatial Information Theory; Cognitive and Computational Foundations of Geographic Information Science, C. Freksa and D.M. Mark, eds., pp. 109-124, 1999.
[25] E. Rich and K. Knight, Artificial Intelligence, Mc-Graw Hill, 1991.
[26] S. Shekhar, A. Fetterer, and B. Goyal, “A Comparison of Hierarchical Algorithms for Shortest Path Computation in Advanced Travel Information Systems,” Technical Report 96-046, Univ. of Minnesota, 1996.
[27] A. Stentz, “Map-Based Strategies for Robot Navigation in Unknown Environments,” Proc. AAAI Symp. Planning with Incomplete Information for Robot Problems, 1996.
[28] C. Thorpe and J. Gowdy, “Annotated Maps for Autonomous Land Vehicles,” Vision and Navigation: The CMU NavLab, 1990.
[29] R.J. Trudeau, Introduction to Graph Theory. New York: Dover, 1993.
[30] J.A. Tupper, “Graphing Equations with Generalized Interval Arithmetic,” PhD thesis, Univ. of Toronto, Canada, 1996.
[31] Q. Yang and J.D. Tenenberg, “Abstraction in Nonlinear Planning,” Technical Report CS-91-65, Univ. of Waterloo, Canada, 1994.
[32] J.Y. Yen, “Finding thekShortest Loopless Paths in a Network,” Management Science, vol. 17, pp. 712-716, 1971.
[33] D. Zhu and J.-C. Latombe, “New Heuristic Algorithms for Efficient Hierarchical Path Planning,” IEEE Trans. Robotics and Automation, vol. 7, no. 1, pp. 9-20, 1991.

Index Terms:
Graph theory, search, hierarchical graphs, path planning.
Juan-Antonio Fernandez-Madrigal, Javier Gonzalez, "Multihierarchical Graph Search," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 1, pp. 103-113, Jan. 2002, doi:10.1109/34.982887
Usage of this product signifies your acceptance of the Terms of Use.