Implicit representation of graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Randomized algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Informative Labeling Schemes for Graphs
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Labeling Schemes for Flow and Connectivity
SIAM Journal on Computing
Proximity-preserving labeling schemes
Journal of Graph Theory
On randomized representations of graphs using short labels
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
An Optimal Labeling for Node Connectivity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Labeling schemes for vertex connectivity
ACM Transactions on Algorithms (TALG)
An O(k^3 log n)-Approximation Algorithm for Vertex-Connectivity Survivable Network Design
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Coding the vertexes of a graph
IEEE Transactions on Information Theory
| Hi-index | 0.89 |
Let G=(V,E) be an undirected graph and let S@?V. The S-connectivity @l"G^S(u,v) of u,v@?V is the maximum number of uv-paths that no two of them have an edge or a node in S@?{u,v} in common. Edge-connectivity is the case S=@A and node-connectivity is the case S=V. Given an integer k and a subset T@?V of terminals, we consider the problem of assigning small ''labels'' (binary strings) to the terminals, such that given the labels of two terminals u,v@?T, one can decide whether @l"G^S(u,v)=k (k-partial labeling scheme) or to return min{@l"G^S(u,v),k} (k-full labeling scheme). We observe that the best known labeling schemes for edge-connectivity (the case S=@A) extend to element-connectivity (the case S@?V@?T), and use it to obtain a simple k-full labeling scheme for node-connectivity (the case S=V). If q distinct queries are expected, our k-full scheme has max-label size O(klog^2|T|logq), with success probability 1-1q for all queries. We also give a deterministic k-full labeling scheme with max-label size O(klog^3|T|). Recently, Hsu and Lu (2009) [6] gave an optimal O(klog|T|) labeling scheme for the k-partial case. This implies an O(k^2log|T|) labeling scheme for the k-full case. Our deterministic k-full labeling scheme is better for k=@W(log^2|T|).