Implicit representation of graphs
SIAM Journal on Discrete Mathematics
Efficient algorithms for finding depth-first and breadth-first search trees in permutation graphs
Information Processing Letters
Simple linear time recognition of unit interval graphs
Information Processing Letters
A linear-time algorithm for proper interval graph recognition
Information Processing Letters
SIAM Journal on Discrete Mathematics
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Graph classes: a survey
Linear-time transitive orientation
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Labeling schemes for small distances in trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Distance Labeling Schemes for Well-Separated Graph Classes
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
On-Line Algorithms for Shortest Path Problems on Planar Digraphs
WG '96 Proceedings of the 22nd 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 Oracles for Reachability and Approximate Distances in Planar Digraphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Journal of Algorithms
Distance and routing labeling schemes for non-positively curved plane graphs
Journal of Algorithms
Proximity-preserving labeling schemes
Journal of Graph Theory
Query efficient implementation of graphs of bounded clique-width
Discrete Applied Mathematics
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
Short labels by traversal and jumping
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Exact distance labelings yield additive-stretch compact routing schemes
DISC'06 Proceedings of the 20th international conference on Distributed Computing
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We show that every comparability graph of any two-dimensional poset over n elements (a.k.a. permutation graph) can be preprocessed in O(n) time, if two linear extensions of the poset are given, to produce an O(n) space data-structure supporting distance queries in constant time. The data-structure is localized and given as a distance labeling, that is each vertex receives a label of O(log n) bits so that distance queries between any two vertices are answered by inspecting on their labels only. As a byproduct, our data-structure supports all-pair shortest-path queries in O(d) time for distance-d pairs, and so identifies in constant time the first edge along a shortest path between any source and destination. More fundamentally, we show that this optimal space and time data-structure cannot be extended for higher dimension posets (we prove that for comparability graphs of three-dimensional posets, every distance labeling scheme requires Ω(n1/3) bit labels).