Local approximation schemes for topology control
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Distributed construction of bounded-degree low-interference spanners of low weight
Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
A simple and efficient kinetic spanner
Computational Geometry: Theory and Applications
As Good as It Gets: Competitive Fault Tolerance in Network Structures
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Reliably detecting connectivity using local graph traits
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Fault Tolerant Spanners for General Graphs
SIAM Journal on Computing
Near-optimal multicriteria spanner constructions in wireless ad hoc networks
IEEE/ACM Transactions on Networking (TON)
Distributed spanner construction in doubling metric spaces
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Sparse fault-tolerant spanners for doubling metrics with bounded hop-diameter or degree
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Fault tolerant additive spanners
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We present two new results about vertex and edge fault-tolerant spanners in Euclidean spaces.We describe the first construction of vertex and edge fault-tolerant spanners having optimal bounds for maximum degree and total cost. We present a greedy algorithm that for any t 1 and any non-negative integer k, constructs a k-fault-tolerant t-spanner in which every vertex is of degree O(k) and whose total cost is O(k2) times the cost of the minimum spanning tree; these bounds are asymptotically optimal.Our next contribution is an efficient algorithm for constructing good fault-tolerant spanners. We present a new, sufficient condition for a graph to be a k-fault-tolerant spanner. Using this condition, we design an efficient algorithm that finds fault-tolerant spanners with asymptotically optimal bound for the maximum degree and almost optimal bound for the total cost.