The input/output complexity of sorting and related problems
Communications of the ACM
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Dealing with higher dimensions: the well-separated pair decomposition and its applications
Dealing with higher dimensions: the well-separated pair decomposition and its applications
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A data structure for dynamically maintaining rooted trees
Journal of Algorithms
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Maintaining hierarchical graph views
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Lower bounds for computing geometric spanners and approximate shortest paths
Discrete Applied Mathematics
Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
Cache Oblivious Distribution Sweeping
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Funnel Heap - A Cache Oblivious Priority Queue
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
t-Spanners as a Data Structure for Metric Space Searching
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
Geometric Spanners for Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
External memory data structures
Handbook of massive data sets
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
I/o-efficient algorithms for shortest path related problems
I/o-efficient algorithms for shortest path related problems
Structural and algorithmic aspects of massive social networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Geometric Spanner Networks
An Optimal Cache-Oblivious Priority Queue and Its Application to Graph Algorithms
SIAM Journal on Computing
Algorithms and data structures for external memory
Foundations and Trends® in Theoretical Computer Science
Randomized and deterministic algorithms for geometric spanners of small diameter
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
I/O-Efficiently pruning dense spanners
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Fast pruning of geometric spanners
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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Given a geometric graph G=(S,E) in R^d with constant dilation t, and a positive constant @e, we show how to construct a (1+@e)-spanner of G with O(|S|) edges using O(sort(|E|)) memory transfers in the cache-oblivious model of computation. The main building block of our algorithm, and of independent interest in itself, is a new cache-oblivious algorithm for constructing a well-separated pair decomposition which builds such a data structure for a given point set S@?R^d using O(sort(|S|)) memory transfers.