The input/output complexity of sorting and related problems
Communications of the ACM
External-memory graph algorithms
Proceedings of the sixth 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
I/O-optimal algorithms for planar graphs using separators
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers & Geosciences - Special issue on GeoComp 99- GeoComputation and the Geosciences
Worst-Case External-Memory Priority Queues
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
The Complexity of Rivers in Triangulated Terrains
Proceedings of the 8th Canadian Conference on Computational Geometry
Digital Elevation Models and TIN Algorithms
Algorithmic Foundations of Geographic Information Systems, this book originated from the CISM Advanced School on the Algorithmic Foundations of Geographic Information Systems
The computational geometry of hydrology data in geographic information systems
The computational geometry of hydrology data in geographic information systems
I/O-efficient point location using persistent B-trees
Journal of Experimental Algorithmics (JEA)
I/O-efficient dynamic planar point location
Computational Geometry: Theory and Applications
I/O-efficient batched union-find and its applications to terrain analysis
Proceedings of the twenty-second annual symposium on Computational geometry
TerraStream: from elevation data to watershed hierarchies
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Computational Geometry: Theory and Applications
External-memory computational geometry
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
An external memory data structure for shortest path queries (extended abstract)
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Flow computations on imprecise terrains
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Exact and approximate computations of watersheds on triangulated terrains
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
A new relative chain code in 3D
Pattern Recognition
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We study the complexity and the i/o-efficient computation of flow on triangulated terrains. We present an acyclic graph, the descent graph, that enables us to trace flow paths in triangulations i/o-efficiently. We use the descent graph to obtain i/o-efficient algorithms for computing river networks and watershed-area maps in O(Sort(d+r))i/o's, where r is the complexity of the river network and d of the descent graph. Furthermore we describe a data structure based on the subdivision of the terrain induced by the edges of the triangulation and paths of steepest ascent and descent from its vertices. This data structure can be used to report the boundary of the watershed of a query point q or the flow path from q in O(l(s)+Scan(k))i/o's, where s is the complexity of the subdivision underlying the data structure, l(s) is the number of i/o's used for planar point location in this subdivision, and k is the size of the reported output. On @a-fat terrains, that is, triangulated terrains where the minimum angle of any triangle is bounded from below by @a, we show that the worst-case complexity of the descent graph and of any path of steepest descent is O(n/@a^2), where n is the number of triangles in the terrain. The worst-case complexity of the river network and the above-mentioned data structure on such terrains is O(n^2/@a^2). When @a is a positive constant this improves the corresponding bounds for arbitrary terrains by a linear factor. We prove that similar bounds cannot be proven for Delaunay triangulations: these can have river networks of complexity @Q(n^3).