Controller and estimator for dynamic networks
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Labeling schemes for weighted dynamic trees
Information and Computation
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ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Note: A note on models for graph representations
Theoretical Computer Science
An Optimal Labeling for Node Connectivity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A sketch-based distance oracle for web-scale graphs
Proceedings of the third ACM international conference on Web search and data mining
Labeling schemes for vertex connectivity
ACM Transactions on Algorithms (TALG)
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
An optimal ancestry scheme and small universal posets
Proceedings of the forty-second ACM symposium on Theory of computing
Compact ancestry labeling schemes for XML trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A note on labeling schemes for graph connectivity
Information Processing Letters
Journal of Parallel and Distributed Computing
Constructing labeling schemes through universal matrices
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Efficient computation of distance sketches in distributed networks
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Labeling schemes for vertex connectivity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Controller and estimator for dynamic networks
Information and Computation
Temporal network optimization subject to connectivity constraints
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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This paper studies labeling schemes for flow and connectivity functions. A flow labeling scheme using $O(\log n\cdot\log {\hat{\omega}}+\log^2 n)$-bit labels is presented for general n-vertex graphs with maximum (integral) capacity ${\hat{\omega}}$. This is shown to be asymptotically optimal. For edge-connectivity, this yields a tight bound of $\Theta(\log^2 n)$ bits. A k-vertex connectivity labeling scheme is then given for general n-vertex graphs using at most 3 log n bits for k = 2, 5 log n bits for k = 3, and 2k log n bits for k 3. Finally, a lower bound of $\Omega (k\log n)$ is established for k -vertex connectivity on n-vertex graphs, where k is polylogarithmic in n.