Orderly Spanning Trees with Applications

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 p...

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Bibliographic Details
Published in:SIAM journal on computing Vol. 34; no. 4; pp. 924 - 945
Main Authors: Chiang, Yi-Ting, Lin, Ching-Chi, Lu, Hsueh-I
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2005
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Data compression
Data processing. List processing. Character string processing
Exact sciences and technology
Graph theory
Graphs
Information retrieval. Graph
Mathematics
Memory organisation. Data processing
Sciences and techniques of general use
Software
Theoretical computing
68P05
Isomorphic graph
Tree(graph)
Realizer
Data compression
Algorithmics
Connected graph
Linear time
68U05
Computing
94C15
Graph drawing
Graph encoding
Data structure
visibility representation
succinct data structure
unit-cost RAM model
Triangulation
68W35
Planar graph
05C85
orderly spanning tree
data compression 05C62
Spanning tree
Canonical ordering
68R10
planar graph algorithm
ISSN:0097-5397, 1095-7111
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0097-5397
1095-7111
DOI:10.1137/S0097539702411381