# A New Link-Based Single Tree Building Algorithm for Shortest Path Searching in an Urban Road Transportation Network

• Suhng, Byung Munn (U-City IT Convergence and Urban Strategy, Graduate School of Hansei University) ;
• Lee, Wangheon (Department of Information Technology, Hansei University)
• Accepted : 2013.05.09
• Published : 2013.07.01
• 90 11

#### Abstract

The shortest-path searching algorithm must not only find a global solution to the destination, but also solve a turn penalty problem (TPP) in an urban road transportation network (URTN). Although the Dijkstra algorithm (DA) as a representative node-based algorithm secures a global solution to the shortest path search (SPS) in the URTN by visiting all the possible paths to the destination, the DA does not solve the TPP and the slow execution speed problem (SEP) because it must search for the temporary minimum cost node. Potts and Oliver solved the TPP by modifying the visiting unit from a node to the link type of a tree-building algorithm like the DA. The Multi Tree Building Algorithm (MTBA), classified as a representative Link Based Algorithm (LBA), does not extricate the SEP because the MTBA must search many of the origin and destination links as well as the candidate links in order to find the SPS. In this paper, we propose a new Link-Based Single Tree Building Algorithm in order to reduce the SEP of the MTBA by applying the breaking rule to the LBA and also prove its usefulness by comparing the proposed with other algorithms such as the node-based DA and the link-based MTBA for the error rates and execution speeds.

#### Keywords

Urban road transportation network;Shortest path searching;Dijksta algorhtm;Link-based algorithm algorithm;$A^*$ algorithm;Dial algorihm

#### Acknowledgement

Supported by : Hansei University

#### References

1. Woo Young Kwon, Il Hong Suh, and Sanghoon Lee," SSPQL: Stochastic Shortest Path-based Q-learning," IJCAS Vol. 9, No. 2, pp.328-338, 2011. https://doi.org/10.1007/s12555-011-0215-2
3. Dijkstra. E. W, "A Note on Two Problems in Connexion with Graphs," Numerische Mathematik Vol. 1, pp. 269-271, 1959. https://doi.org/10.1007/BF01386390
4. R. B. Potts, R. M. Oliver, "Flows in Transportation Networks," Academic Press, pp. 61, 1972.
5. Hart. P. E, Nilsson. N. J, Raphael. B, "A Formal Basis for the Heuristic Determination of Minimum Cost Paths," IEEE Transactions on Systems Science and Cybernetics, Vol. SSC4, pp. 100-107, 1968.
6. R. Dial, "Shortest path forest with topological ordering," Algorithm 360, Communications of the ACM, Vol. 12 pp. 632-633, 1969. https://doi.org/10.1145/363269.363610
7. R. Bellman, "Dynamic Programming," Princeton University Press, 1957.
8. R. Bellman, "On a Routing Problem," Quarterly of Applied Mathematics, Vol. 16, pp. 87-90, 1958. https://doi.org/10.1090/qam/102435
9. Thomas H. Cormen, "Introduction To Algorithm," 3rd, edition, MIT Press, pp. 643-684, 2009.
10. Ravindra K. Ahuja, "Network Flows," Sloan W.P. No. 2059-88, MIT Press. pp. 55, 1998.
11. Ford. L. R, Fulkerson, "Flows in Networks," Princeton University Press, 1962.
12. E. Moore, "The Annals of the Computation Laboratory of Harvard University," Vol. 30. Cambridge Mass. Harvard University Press, 1959.
13. Park. D, "Multiple Path Based Vehicle Routing in Dynamic and Stochastic.
14. Ravindra K. Ahuja, "Faster Algorithms for shortest path problem," Sloan W. P. No. 2043-88, MIT Press, 1998.