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Discrete & Computational Geometry
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Efficient algorithms for constructing fault-tolerant geometric spanners
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STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
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STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Randomized and deterministic algorithms for geometric spanners of small diameter
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
I/O-Efficient Batched Range Counting and Its Applications to Proximity Problems
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
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
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SIAM Journal on Computing
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Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
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International Journal of Network Management
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ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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We investigate the problem of constructing spanners for a given set of points that are tolerant for edge/vertex faults. Let S ⊂ IRd be a set of n points and let k be an integer number. A k-edge/vertex fault tolerant spanner for S has the property that after the deletion of k arbitrary edges/vertices each pair of points in the remaining graph is still connected by a short path. Recently it was shown that for each set S of n points there exists a k-edge/vertex fault tolerant spannerwith O(k2n) edges which can be constructed in O(nlogn+ k2n) time. Furthermore, it was shown that for each set S of n points there exists a k-edge/vertex fault tolerant spannerwhose degree is bouned by O(ck+1) for some constant c. Our first contribution is a construction of a k-vertex fault tolerant spanner with O(kn) edges which is a tight bound. The computation takes O(nlogd-1n + knloglogn) time. Then we show that the same k-vertex fault tolerant spanner is also k-edge fault tolerant. Thereafter, we construct a k-vertex fault tolerant spanner with O(k2n) edges whose degree is bounded by O(k2). Finally, we give a more natural but stronger definition of k-edge fault tolerance which not necessarily can be satisfied if one allows only simple edges between the points of S. We investigate the question whether Steiner points help. We answer this question affirmatively and prove ⊖(kn) bounds on the number of Steiner points and on the number of edges in such spanners.