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We present a technique for representing bounded-degree planar graphs in a succinct fashion while permitting I/O-efficient traversal of paths. Using our representation, a graph with N vertices, (In this paper $$\lg {N}$$ lg N denotes $$\log _2{N}$$ log 2 N ) each with an associated key of $$q= \mathrm {O}\left( \lg N\right) $$ q = O lg N bits, can be stored in ...
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...
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