Intersection graphs of paths in a tree
Journal of Combinatorial Theory Series B
A new approach to all pairs shortest paths in planar graphs
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Labeling schemes for flow and connectivity
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Labeling schemes for small distances in trees
SODA '03 Proceedings of the fourteenth 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
Short and Simple Labels for Small Distances and Other Functions
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Distance Labeling Schemes for Well-Separated Graph Classes
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Labeling Schemes for Dynamic Tree Networks
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
Graph compression and the zeros of polynomials
Information Processing Letters
Journal of Algorithms
Distance labeling schemes for well-separated graph classes
Discrete Applied Mathematics
Informative labeling schemes for graphs
Theoretical Computer Science - Mathematical foundations of computer science 2000
Distance and routing labeling schemes for non-positively curved plane graphs
Journal of Algorithms
Adjacency queries in dynamic sparse graphs
Information Processing Letters
Average case analysis for tree labelling schemes
Theoretical Computer Science
On local representation of distances in trees
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Engineering Tree Labeling Schemes: A Case Study on Least Common Ancestors
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Representation of graphs by OBDDs
Discrete Applied Mathematics
A bi-labeling based XPath processing system
Information Systems
As Good as It Gets: Competitive Fault Tolerance in Network Structures
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
An implicit representation of chordal comparability graphs in linear time
Discrete Applied Mathematics
Labeling schemes for weighted dynamic trees
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Shorter implicit representation for planar graphs and bounded treewidth graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Distributed relationship schemes for trees
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A note on labeling schemes for graph connectivity
Information Processing Letters
Short labels by traversal and jumping
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Average case analysis for tree labelling schemes
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
General compact labeling schemes for dynamic trees
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Approximation scheme for lowest outdegree orientation and graph density measures
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Sorting, searching, and simulation in the mapreduce framework
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an n-node graph, the names of the nodes (i.e. integers from 1 to n) betray nothing about the graph itself. Indeed, the names (or labels) on the n nodes are just logn bit place holders to allow data on the edges to code for the structure of the graph. In our scenario, there is no such waste. By assigning &Ogr;(logn) bit labels to the nodes, we completely code for the structure of the graph, so that given the labels of two nodes we can test if they are adjacent in time linear in the size of the labels. Furthermore, given an arbitrary original labeling of the nodes, we can find structure coding labels (as above) that are no more than a small constant factor larger than the original labels. These notions are intimately related to vertex induced universal graphs of polynomial size. For example, we can label planar graphs with structure coding labels of size n. This implies the existence of a graph with n4 nodes that contains all n-node planar graphs as vertex induced subgraphs (It was not previously known that this class had polynomial sized universal graphs). The theorems on finite graphs extend to a theorem about the constrained labeling of infinite graphs.