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An external memory data structure for shortest path queries (Extended Abstract)
, 2003
"... We present results related to satisfying shortest path queries on a planar graph stored in external memory. In particular, we show how to store rooted trees in external memory so that bottomup paths can be traversed I/Oefficiently, and we present I/Oefficient algorithms for triangulating planar ..."
Abstract

Cited by 23 (7 self)
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We present results related to satisfying shortest path queries on a planar graph stored in external memory. In particular, we show how to store rooted trees in external memory so that bottomup paths can be traversed I/Oefficiently, and we present I/Oefficient algorithms for triangulating planar graphs and computingsmall separators of such graphs. Using these techniques, we can construct a data structure that allows for answering shortest path queries on a planar graph I/Oefficiently.
An ExternalMemory Data Structure for Shortest Path Queries
, 1999
"... 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 desc ..."
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Cited by 11 (1 self)
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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 bottomup 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 breadthfirst 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 ...
I/OOptimal Planar Embedding Using Graph Separators
, 2001
"... We present a new algorithm to test whether a given graph G is planar and to compute a planar embedding G of G if such an embedding exists. Our algorithm utilizes a fundamentally new approach based on graph separators to obtain such an embedding. The I/Ocomplexity of our algorithm is O(sort(N)). A s ..."
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Cited by 1 (0 self)
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We present a new algorithm to test whether a given graph G is planar and to compute a planar embedding G of G if such an embedding exists. Our algorithm utilizes a fundamentally new approach based on graph separators to obtain such an embedding. The I/Ocomplexity of our algorithm is O(sort(N)). A simple simulation technique reduces the I/Ocomplexity of our algorithm to O(perm(N)). We prove a matching lower bound of W(perm(N)) I/Os for computing a planar embedding of a given planar graph.