An external memory data structure for shortest path queries

  • Authors:

  • David Hutchinson;Anil Maheshwari;Norbert Zeh

  • Affiliations:

  • Department of Computer Science, Duke University, Durham, NC;School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ont., Canada K1S 5B6;School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ont., Canada K1S 5B6

  • Venue:
  • Discrete Applied Mathematics - Special issue: Special issue devoted to the fifth annual international computing and combinatories conference (COCOON'99) Tokyo, Japan 26-28 July 1999
  • Year:
  • 2003

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Abstract

We present results related to satisfying shortest path queries on a planar graph stored in external memory. Let N denote the number of vertices in the graph and sort(N) denote the number of input/output (I/O) operations required to sort an array of length N: (1) We describe a blocking for rooted trees to support bottom-up traversals of these trees in O(K/B) I/Os, where K is the length of the traversed path. The space required to store the tree is O(N/B) blocks, where N is the number of vertices of the tree and B is the block size. (2) We give an algorithm for computing a 2/3-separator of size O(√N) for a given embedded planar graph. Our algorithm takes O(sort(N)) I/Os, provided that a breadth-first spanning tree is given. (3) We give an algorithm for triangulating embedded planar graphs in O(sort(N)) I/Os. We use these results to construct a data structure for answering shortest path queries on planar graphs. The data structure uses O(N3/2/B) blocks of external memory and allows for a shortest path query to be answered in O((√N + K)/DB) I/Os, where K is the number of vertices on the reported path and D is the number of parallel disks.