Compact routing with minimum stretch
Journal of Algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Proximity-Preserving Labeling Schemes and Their Applications
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Compact routing with name independence
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
All pairs almost shortest paths
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
Journal of Algorithms
Distance labeling schemes for well-separated graph classes
Discrete Applied Mathematics
New constructions of (α, β)-spanners and purely additive spanners
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Localized and compact data-structure for comparability graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
On compact and efficient routing in certain graph classes
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Collective tree spanners and routing in AT-free related graphs
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
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Distance labelings and compact routing schemes have both been active areas of recent research. It was already known that graphs with constant-sized recursive separators, such as trees, outerplanar graphs, series-parallel graphs and graphs of bounded treewidth, support both exact distance labelings and optimal (additive stretch 0, multiplicative stretch 1) compact routing schemes, but there are many classes of graphs known to admit exact distance labelings that do not have constant-sized separators. Our main result is to demonstrate that every unweighted, undirected n-vertex graph which supports an exact distance labeling with l(n)-sized labels also supports a compact routing scheme with O(l(n) + log2n/loglogn)-sized headers, $O(\sqrt{n}(l(n) + \log^2{n}/\log{\log{n}}))$-sized routing tables, and an additive stretch of 6. We then investigate two classes of graphs which support exact distance labelings (but do not guarantee constant-sized separators), where we can improve substantially on our general result. In the case of interval graphs, we present a compact routing scheme with O(logn)-sized headers, O(logn)-sized routing tables and additive stretch 1, improving headers and table sizes from a result of [1], which uses O(log3n/loglogn)-bit headers and tables. We also present a compact routing scheme for the related family of circular arc graphs which guarantees O(log2n)-sized headers, O(logn)-sized routing tables and an additive stretch of 1.