On shortest paths amidst convex polyhedra
SIAM Journal on Computing
A bridging model for parallel computation
Communications of the ACM
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
On finding and updating shortest paths distributively
Journal of Algorithms
The one-to-one shortest-path problem: an empirical analysis with the two-tree Dijkstra algorithm
Computational Optimization and Applications
Parallel shortest path auction algorithms
Parallel Computing
On the shortest paths between two convex polyhedra
Journal of the ACM (JACM)
Parallel asynchronous label-correcting methods for shortest paths
Journal of Optimization Theory and Applications
Approximating shortest paths on a convex polytope in three dimensions
Proceedings of the twelfth annual symposium on Computational geometry
Parallel neighbourhood modelling
GIS '96 Proceedings of the 4th ACM international workshop on Advances in geographic information systems
Approximating shortest paths on a convex polytope in three dimensions
Journal of the ACM (JACM)
Handbook of discrete and computational geometry
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Practical methods for approximating shortest paths on a convex polytope in R3
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Buckets Strike Back: Improved Parallel Shortest Paths
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
An epsilon-Approximation for Weighted Shortest Paths on Polyhedral Surfaces
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Approximating Shortest Paths on a Nonconvex Polyhedron
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Shortest path problems on polyhedral surfaces
Shortest path problems on polyhedral surfaces
Calculating the meeting point of scattered robots on weighted terrain surfaces
CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
Computing an approximation of the 1-center problem on weighted terrain surfaces
Journal of Experimental Algorithmics (JEA)
A theoretical approach to the use of cyberinfrastructure in geographical analysis
International Journal of Geographical Information Science
A survey of geodesic paths on 3D surfaces
Computational Geometry: Theory and Applications
Data-Parallel method for georeferencing of MODIS level 1b data using grid computing
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Environmental Modelling & Software
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In application areas such as geographical information systems, the Euclidean metric is often less meaningfully applied to determine a shortest path than metrics which capture, through weights, the varying nature of the terrain (e.g., water, rock, forest). Considering weighted metrics, however, increases the run-time of algorithms considerably suggesting the use of a parallel approach. In this paper, we provide a parallel implementation of shortest path algorithms for the Euclidean and weighted metrics on triangular irregular networks (i.e., a triangulated point set in which each point has an associated height value). To the best of our knowledge, this is the first parallel implementation of shortest path problems in these metrics. We provide a detailed discussion of the algorithmic issues and the factors related to data, machine, implementation which determine the performance of parallel shortest path algorithms. We describe our parallel algorithm for weighted shortest paths, its implementation and performance for single-and multiple-source instances. Our experiments were performed on standard architectures with different communication/computation characteristics, including PCs interconnected by a cross-bar switch using fast ethernet, a state-of-the-art Beowulf cluster with gigabit interconnect and a shared-memory architecture, SunFire.