Local structure in graph classes
Local structure in graph classes
Implicit representation of graphs
SIAM Journal on Discrete Mathematics
Graph classes: a survey
An Optimal Algorithm to Detect a Line Graph and Output Its Root Graph
Journal of the ACM (JACM)
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
Nearest common ancestors: a survey and a new distributed algorithm
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Informative Labeling Schemes for Graphs
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Dynamic Representation of Sparse Graphs
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Short and Simple Labels for Small Distances and Other Functions
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Proximity-Preserving Labeling Schemes and Their Applications
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Labeling schemes for weighted dynamic trees
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Adjacency queries in dynamic sparse graphs
Information Processing Letters
| Hi-index | 0.01 |
As defined by Muller (Muller, Ph.D. thesis, Georgia Tech, 1988) and Kannan, Naor, and Rudich (Kannan et al., SIAM J Disc Math, 1992), an adjacency labelling scheme labels the vertices of a graph so the adjacency of two vertices can be deduced implicitly from their labels. In general, the labels used in adjacency labelling schemes cannot be tweaked to reflect small changes in the graph. Motivated by the necessity for further exploration of dynamic (implicit) adjacency labelling schemes we introduce the concept of error detection, discuss metrics for judging the quality of such dynamic schemes, and develop a dynamic scheme for line graphs that allows the addition and deletion of vertices and edges. The labels used in this scheme require O(log n) bits and updates can be performed in O(e) time, where e is the number of edges added to or deleted from the line graph. This compares to the best known (static) adjacency labelling scheme for line graphs which uses O(log n) bit labels and requires Θ(n) time to generate a labelling even when provided with the line graph representation.