Four pages are necessary and sufficient for planar graphs
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The page number of genus g graphs is (g)
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
Faster shortest-path algorithms for planar graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Short encodings of planar graphs and maps
Discrete Applied Mathematics
Memory requirement for routing in distributed networks
PODC '96 Proceedings of the fifteenth annual ACM symposium on Principles of distributed computing
Compact routing schemes with low stretch factor (extended abstract)
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Succinct representation of balanced parentheses, static trees and planar graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Genus g graphs have pagenumber O( square root g)
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Improved Compact Routing Scheme for Chordal Graphs
DISC '02 Proceedings of the 16th International Conference on Distributed Computing
An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
An Additive Stretched Routing Scheme for Chordal Graphs
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees
SIAM Journal on Discrete Mathematics
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Navigating in a Graph by Aid of Its Spanning Tree Metric
SIAM Journal on Discrete Mathematics
Planar graphs, via well-orderly maps and trees
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Compact routing for graphs excluding a fixed minor
DISC'05 Proceedings of the 19th international conference on Distributed Computing
A compact routing scheme and approximate distance oracle for power-law graphs
ACM Transactions on Algorithms (TALG)
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For planar graphs on n nodes we show how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log2+Ɛ n) bit-operations per node to extract the route, with constant Ɛ 0. We generalize the result for every graph of bounded crossing-edge number. We also extend our result to any graph of genus bounded by γ, by building shortest path routing tables of n log (γ + 1)+ O(n) bits per node, and with O(log2+Ɛ n) bit-operations per node to extract the route. This result is obtained by the use of dominating sets, compact coding of non-crossing partitions, and k-page representation of graphs.