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Write it recursively: a generic framework for optimal path queries

Published:20 September 2008Publication History

ABSTRACT

Optimal path queries are queries to obtain an optimal path specified by a given criterion of optimality. There have been many studies to give efficient algorithms for classes of optimal path problem. In this paper, we propose a generic framework for optimal path queries. We offer a domain-specific language to describe optimal path queries, together with an algorithm to find an optimal path specified in our language. One of the most distinct features of our framework is the use of recursive functions to specify queries. Recursive functions reinforce expressiveness of our language so that we can describe many problems including known ones; thus, we need not learn existing results. Moreover, we can derive an efficient querying algorithm from the description of a query written in recursive functions. Our algorithm is a generalization of existing algorithms, and answers a query in O(n log n) time on a graph of O(n) size. We also explain our implementation of an optimal path querying system, and report some experimental results.

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  1. Christopher L. Barrett, Riko Jacob, and Madhav V. Marathe. Formal-language-constrained path problems. SIAM Journal on Computing, 30(3):809--837, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Christopher L. Barrett, Keith Bisset, Riko Jacob, Goran Konjevod, and Madhav V. Marathe. Classical and contemporary shortest path problems in road networks: Implementation and experimental analysis of the TRANSIMS router. In Algorithms - ESA 2002, 10th Annual European Symposium, Rome, Italy, September 17-21, 2002, Proceedings, volume 2461 of Lecture Notes in Computer Science, pages 126--138. Springer, 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Christopher L. Barrett, Keith Bisset, Riko Jacob, Goran Konjevod, Madhav V. Marathe, and Dorothea Wagner. Label constrained shortest path algorithms: An experimental evaluation using transportation networks. Technical report, Virginia Tech (USA), Arizona State University (USA), and Karlsruhe University (Germany), 2007.Google ScholarGoogle Scholar
  4. Richard Bellman. Dynamic Programming. Princeton University Press, 1957. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Gerth Stølting Brodal and Riko Jacob. Time-dependent networks as models to achieve fast exact time-table queries. Electronic Notes in Theoretical Computer Science, 92:3--15, 2004.Google ScholarGoogle ScholarCross RefCross Ref
  6. Edward P. F. Chan and Jie Zhang. A fast unified optimal route query evaluation algorithm. In Proceedings of the Sixteenth ACM Conference on Information and Knowledge Management, CIKM 2007, Lisbon, Portugal, November 6-10, 2007, pages 371--380. ACM, 2007. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Oege de Moor, David Lacey, and Eric Van Wyk. Universal regular path queries. Higher-Order and Symbolic Computation, 16(1-2):15--35, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Martin Desrochers and François Soumis. A generalized permanent labeling algorithm for the shortest path problem with time windows. INFOR, 26:191--212, 1988.Google ScholarGoogle Scholar
  9. David Eppstein. Finding the k shortest paths. SIAM Journal on Computing, 28(2):652--673, 1998. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Sergio Flesca, Filippo Furfaro, and Sergio Greco. Weighted path queries on semistructured databases. Information and Computation, 204(5):679--696, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Toshihide Ibaraki. Solvable classes of discrete dynamic programming. Journal of mathematical analysis and applications, 43(3):642--693, 1973.Google ScholarGoogle Scholar
  12. Toshihide Ibaraki. Branch-and-bound procedure and state-space representation of combinatorial optimization problems. Information and Control, 36(1):1--27, 1978.Google ScholarGoogle ScholarCross RefCross Ref
  13. Donald B. Johnson. Efficient algorithms for shortest paths in sparse networks. Journal of the ACM, 24(1):1--13, 1977. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. H. C. Joksch. The shortest route problem with constraints. Journal of Mathematical analysis and applications, 14:191--197, 1966.Google ScholarGoogle Scholar
  15. Richard M. Karp and Michael Held. Finite-state processes and dynamic programming. SIAM Journal on Applied Mathematics, 15(3):693--718, 1967.Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Turgay Korkmaz and Marwan Krunz. Multi-constrained optimal path selection. In Proceedings IEEE INFOCOM 2001, The Conference on Computer Communications, Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies, pages 834--843, 2001.Google ScholarGoogle ScholarCross RefCross Ref
  17. Yanhong A. Liu, Tom Rothamel, Fuxiang Yu, Scott D. Stoller, and Nanjun Hu. Parametric regular path queries. In Proceedings of the ACM SIGPLAN 2004 Conference on Programming Language Design and Implementation 2004, Washington, DC, USA, June 9-11, 2004, pages 219--230. ACM, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Ernesto Q. Vieira Martins. An algorithm for ranking paths that may contain cycles. European Journal of Operational Research, 18(1):123--130, 1984.Google ScholarGoogle ScholarCross RefCross Ref
  19. Alberto O. Mendelzon and Peter T. Wood. Finding regular simple paths in graph databases. SIAM Jornal on Computing, 24(6):1235--1258, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Akimasa Morihata, Kiminori Matsuzaki, Zhenjiang Hu, and Masato Takeichi. Calculus of minimals: Deriving dynamic-programming algorithms based on preservation of monotonicity. Technical Report METR 2007-61, Department of Mathematical Informatics, University of Tokyo, 2007.Google ScholarGoogle Scholar
  21. Mizuhito Ogawa, Zhenjiang Hu, and Isao Sasano. Iterative-free program analysis. In Proceedings of the Eighth ACM SIGPLAN International Conference on Functional Programming, ICFP'03, Uppsala, Sweden, August 25-29, 2003, pages 111--123. ACM, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Abraham P. Punnen. A linear time algorithm for the maximum capacity path problem. European Journal of Operational Research, 53(3):402--404, 1991.Google ScholarGoogle ScholarCross RefCross Ref
  23. Jean-François Romeuf. Shortest path under rational constraint. Information Processing Letters, 28(5):245--248, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Isao Sasano, Zhenjiang Hu, Masato Takeichi, and Mizuhito Ogawa. Make it practical: a generic linear-time algorithm for solving maximumweightsum problems. In Proceedings of the 5th ACM SIGPLAN International Conference on Functional Programming, ICFP'00, pages 137--149. ACM, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Hanif D. Sherali, Chawalit Jeenanunta, and Antoine G. Hobeika. The approach-dependent, time-dependent, label-constrained shortest path problem. Networks, 48(2):57--67, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Jeremy G. Siek, Lie-Quan Lee, and Andrew Lumsdaine. The Boost Graph Library: User Guide and Reference Manual. Addison-Wesley, 2001.Google ScholarGoogle Scholar
  27. Daniel Villeneuve and Guy Desaulniers. The shortest path problem with forbidden paths. European Journal of Operational Research, 165(1):97--107, 2005.Google ScholarGoogle ScholarCross RefCross Ref

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