Abstract

In this paper, we present results related to satisfying shortest path queries on a planar graph stored in external memory. N denotes the total number of vertices and edges in the graph and sort(N) denotes the number of input/output (I/O) operations required to sort an array of length N . 1) We describe a data structure for supporting bottom-up traversal of rooted trees in external memory. A tree of size S is stored in O(S=B) blocks, and traversing a path of length K towards the root in this tree takes O(K=B) I/Os. 2) We give an algorithm for computing a separator for an embedded planar graph in O(sort(N)) I/Os, provided that a breadth-first search (BFS) tree is given. 3) We describe an algorithm for triangulating an embedded planar graph in O(sort(N)) I/Os. Using these results, we can obtain a data structure for shortest path queries on graphs with separators of size O( p N) that uses O(N 3=2 =B) blocks of external memory and allows for answering shortest path queries in O(( p ...

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