Succinct ordinal trees with level-ancestor queries
ACM Transactions on Algorithms (TALG)
Ultra-succinct representation of ordered trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Balanced parentheses strike back
ACM Transactions on Algorithms (TALG)
Succinct geometric indexes supporting point location queries
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
I/O and Space-Efficient Path Traversal in Planar Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A compact encoding of plane triangulations with efficient query supports
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
A compact encoding of plane triangulations with efficient query supports
Information Processing Letters
Fully-functional succinct trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees
SIAM Journal on Discrete Mathematics
Engineering the LOUDS succinct tree representation
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
Ultra-succinct representation of ordered trees with applications
Journal of Computer and System Sciences
Succinct geometric indexes supporting point location queries
ACM Transactions on Algorithms (TALG)
Bounding the number of reduced trees, cographs, and series-parallel graphs by compression
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Succinct ordinal trees based on tree covering
ACM Transactions on Algorithms (TALG)
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We introduce and study orderly spanning trees of plane graphs. This algorithmic tool generalizes canonical orderings, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an orderly pair for any connected planar graph G, consisting of an embedded planar graph H isomorphic to G, and an orderly spanning tree of H. We also present several applications of orderly spanning trees: (1) a new constructive proof for Schnyder's realizer theorem, (2) the first algorithm for computing an area-optimal 2-visibility drawing of a planar graph, and (3) the most compact known encoding of a planar graph with O(1)-time query support. All algorithms in this paper run in linear time.