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<p><b>Abstract</b>—In this paper, we have developed a <tmath>\big. HiTi\bigr.</tmath> (Hierarchical MulTi) graph model for structuring large topographical road maps to speed up the minimum cost route computation. The <tmath>\big. HiTi\bigr.</tmath> graph model provides a novel approach to abstracting and structuring a topographical road map in a hierarchical fashion. We propose a new shortest path algorithm named <tmath>\big. SPAH\bigr.</tmath>, which utilizes <tmath>\big. HiTi\bigr.</tmath> graph model of a topographical road map for its computation. We give the proof for the optimality of <tmath>\big. SPAH\bigr.</tmath>. Our performance analysis of <tmath>\big. SPAH\bigr.</tmath> on grid graphs showed that it significantly reduces the search space over existing methods. We also present an in-depth experimental analysis of HiTi graph method by comparing it with other similar works on grid graphs. Within the <tmath>\big. HiTi\bigr.</tmath> graph framework, we also propose a parallel shortest path algorithm named <tmath>\big. ISPAH\bigr.</tmath>. Experimental results show that <it>inter</it> query shortest path problem provides more opportunity for scalable parallelism than the <it>intra</it> query shortest path problem.</p>
Shortest Path, digital road maps, grid graphs, parallel shortest path computation, HiTi graph model.

S. Jung and S. Pramanik, "An Efficient Path Computation Model for Hierarchically Structured Topographical Road Maps," in IEEE Transactions on Knowledge & Data Engineering, vol. 14, no. , pp. 1029-1046, 2002.
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