On the convex hull of the integer points in a disc
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
WG '92 Proceedings of the 18th International Workshop on Graph-Theoretic Concepts in Computer Science
Island hopping and path colouring with applications to WDM network design
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Transitive-closure spanners: a survey
Property testing
Transitive-closure spanners: a survey
Property testing
Efficient provably-secure hierarchical key assignment schemes
Theoretical Computer Science
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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A conjecture by Thorup is that the diameter of a directed graph with n vertices and m edges can be reduced to (log n)O(1) by adding O(m) edges [3]. We give a counterexample to this conjecture. We construct a graph G requiring the addition of Ω(mn 1/17) edges to reduce its diameter below Θ(n1/17). By extending the construction to higher dimensions, we construct graphs with n1+ε edges that require the addition of Ω(n2--ε) edges to reduce their diameter. These constructions yield time-space tradeoffs in lower bounds for transitive closure queries in a certain computational model.