Implicit representation of graphs
SIAM Journal on Discrete Mathematics
Compact labeling schemes for ancestor queries
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Labeling schemes for flow and connectivity
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Reachability and distance queries via 2-hop labels
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved labeling scheme for ancestor queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A comparison of labeling schemes for ancestor queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Small Induced-Universal Graphs and Compact Implicit Graph Representations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Short and Simple Labels for Small Distances and Other Functions
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
A Space Lower Bound for Routing in Trees
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Proximity-Preserving Labeling Schemes and Their Applications
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Approximate Distance Labeling Schemes
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Labeling Schemes for Flow and Connectivity
SIAM Journal on Computing
Journal of Algorithms
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Distance labeling schemes for well-separated graph classes
Discrete Applied Mathematics
Labeling Schemes for Small Distances in Trees
SIAM Journal on Discrete Mathematics
Informative labeling schemes for graphs
Theoretical Computer Science - Mathematical foundations of computer science 2000
Average case analysis for tree labelling schemes
Theoretical Computer Science
Labeling schemes for weighted dynamic trees
Information and Computation
Labeling Schemes for Tree Representation
Algorithmica
Labeling schemes for vertex connectivity
ACM Transactions on Algorithms (TALG)
Compact ancestry labeling schemes for XML trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Constructing labeling schemes through universal matrices
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Labeling schemes for vertex connectivity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
A note on labeling schemes for graph connectivity
Information Processing Letters
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Given an n-node undirected simple graph G and a positive integer k, the k-connectivity labeling problem for G seeks short labels for the nodes of G such that whether any two nodes are k-connected in G can be determined merely by their labels. For k = 1, an optimal solution to the problem is to give each node in the same connected component of G a common 驴log2 n驴-bit label, uniquely chosen for this connected component. For k 驴 2, Katz, Katz, Korman, and Peleg gave the first nontrivial solution to the problem, requiring O(2 k logn) bits per node. The best previously known solution, due to Korman, requires O(k 2logn) bits per node. We give the first asymptotically optimal solution to the problem, requiring only $(2k-1)\left\lceil\log_2 n\right\rceil$ bits per node, which matches a lower bound 驴(klogn) proved by Katz, Katz, Korman, and Peleg.