Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
The input/output complexity of sorting and related problems
Communications of the ACM
Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
I/O-efficient algorithms for contour-line extraction and planar graph blocking
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Succinct indexable dictionaries with applications to encoding k-ary trees and multisets
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Complexity of Rivers in Triangulated Terrains
Proceedings of the 8th Canadian Conference on Computational Geometry
Succinct representation of balanced parentheses, static trees and planar graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Orderly Spanning Trees with Applications
SIAM Journal on Computing
Geometric Burrows-Wheeler Transform: Linking Range Searching and Text Indexing
DCC '08 Proceedings of the Data Compression Conference
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Succinct geometric indexes supporting point location queries
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Succinct and I/O Efficient Data Structures for Traversal in Trees
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
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We present a technique for representing bounded-degree planar graphs succinctly while permitting I/O-efficient path traversal. To represent a graph G on N vertices, each with an associated key of $q = O(\lg{N})$ bits, we use Nq + O(N) + o(Nq) bits. Using this representation, a path of length K can be traversed with $O(K/ \lg {B})$ I/Os, where B is the disk block size. Our structure may be adapted to represent, with similar space bounds, a terrain modeled as a triangular-irregular network to support traversal of a path that visits K triangles using $O(K/ \lg {B})$ I/Os. This structure can be used to answer a number of useful queries efficiently, such as reporting terrain profiles, trickle paths and connected components.