A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
An optimal synchronizer for the hypercube
SIAM Journal on Computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Parallel shortcutting of rooted trees
Journal of Algorithms
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Communication-time trade-offs in network synchronization
Proceedings of the fourth annual ACM symposium on Principles of distributed computing
Polylog-time and near-linear work approximation scheme for undirected shortest paths
Journal of the ACM (JACM)
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Compact routing with minimum stretch
Journal of Algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Roundtrip spanners and roundtrip routing in directed graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Trade-offs in non-reversing diameter
Nordic Journal of Computing
Directed graphs requiring large numbers of shortcuts
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Strong Inapproximability of the Basic k-Spanner Problem
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Improved Testing Algorithms for Monotonicity
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
WG '92 Proceedings of the 18th International Workshop on Graph-Theoretic Concepts in Computer Science
Space-time tradeoff for answering range queries (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Compact roundtrip routing in directed networks
Journal of Algorithms
On the strength of comparisons in property testing
Information and Computation
Journal of the ACM (JACM)
Dynamic and efficient key management for access hierarchies
Proceedings of the 12th ACM conference on Computer and communications security
Key management for non-tree access hierarchies
Proceedings of the eleventh ACM symposium on Access control models and technologies
Object location using path separators
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Lower Bounds for Additive Spanners, Emulators, and More
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
Information theory in property testing and monotonicity testing in higher dimension
Information and Computation
The Hardness of Approximating Spanner Problems
Theory of Computing Systems
Parallel monotonicity reconstruction
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Property-Preserving Data Reconstruction
Algorithmica
Dynamic and Efficient Key Management for Access Hierarchies
ACM Transactions on Information and System Security (TISSEC)
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Fast approximate PCPs for multidimensional bin-packing problems
Information and Computation
Lower bounds for local monotonicity reconstruction from transitive-closure spanners
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Efficient provably-secure hierarchical key assignment schemes
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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We survey results on transitive-closure spanners and their applications. Given a directed graph G = (V, E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V, EH) that has (1) the same transitive-closure as G and (2) diameter at most k. These spanners were studied implicitly in different areas of computer science, and properties of these spanners have been rediscovered over the span of 20 years. The common task implicitly tackled in these diverse applications can be abstracted as the problem of constructing sparse TC-spanners. In this article, we survey combinatorial bounds on the size of sparsest TC-spanners, and algorithms and inapproximability results for the problem of computing the sparsest TC-spanner of a given directed graph. We also describe multiple applications of TC-spanners, including property testing, property reconstruction, key management in access control hierarchies and data structures.