A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
On sparse spanners of weighted graphs
Discrete & Computational Geometry
NP-completeness of minimum spanner problems
Discrete Applied Mathematics
SIAM Journal on Discrete Mathematics
Explicit construction of graphs with an arbitrary large girth and of large size
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
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Information and Computation
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A High Girth Graph Construction
SIAM Journal on Discrete Mathematics
A simple linear time algorithm for computing a (2k - 1)-spanner of o(n1+1/k) size in weighted graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Fast pruning of geometric spanners
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Computing a minimum-dilation spanning tree is NP-hard
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Computing a minimum-dilation spanning tree is NP-hard
Computational Geometry: Theory and Applications
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CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Computing geometric minimum-dilation graphs is NP-hard
GD'06 Proceedings of the 14th international conference on Graph drawing
Spanners of complete k-partite geometric graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Improved multi-criteria spanners for ad-hoc networks under energy and distance metrics
INFOCOM'10 Proceedings of the 29th conference on Information communications
Near-optimal multicriteria spanner constructions in wireless ad hoc networks
IEEE/ACM Transactions on Networking (TON)
Improved multicriteria spanners for Ad-Hoc networks under energy and distance metrics
ACM Transactions on Sensor Networks (TOSN)
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Given a connected geometric graph G, we consider the problem of constructing a t-spanner of G having the minimum number of edges. We prove that for every t with $1 G with n vertices, such that every t-spanner of G contains Ω( n1+1/t ) edges. This bound almost matches the known upper bound, which states that every connected weighted graph with n vertices contains a t-spanner with O(tn1+2/(t+1)) edges. We also prove that the problem of deciding whether a given geometric graph contains a t-spanner with at most K edges is NP-hard. Previously, this NP-hardness result was only known for non-geometric graphs