novel application
1999
chapter
node π
methodology
https://doi.org/10.1007/3-540-48481-7_47
distinct node (respectively, edge) labels
’s census series
string x
set of properties
planar graphs
general methodology
2022-01-01T19:17
labels
graph
set
https://scigraph.springernature.com/explorer/license/
chapters
separator
simple planar graph
minimum number
graph G
true
conjunction
plane graph
node labels
class
properties
example
paper
540-549
applications
Fast General Methodology
information
general class
en
satisfies certain properties
Tutte’s census series
A Fast General Methodology for Information—Theoretically Optimal Encodings of Graphs
series
1999-01-01
cycle separator
binary string x
property π
encoding
number
function
certain properties
bits
time
problem
small cycle separators
We propose a fast methodology for encoding graphs with informationtheoretically minimum numbers of bits. The methodology is applicable to general classes of graphs; this paper focuses on simple planar graphs. Specifically, a graph with property π is called a π-graph. If π satisfies certain properties, then an n-node π-graph G can be encoded by a binary string X such that (1) G and X can be obtained from each other in O(n log n) time, and (2)X has at most β(n)+ o(β(n)) bits for any function β(n) = Ω (n) so that there are at most 2β(n)+ o(β(n)) distinct n-node π-graphs. Examples of such π include all conjunctions of the following sets of properties: (1) G is a planar graph or a plane graph; (2) G is directed or undirected; (3) G is triangulated, triconnected, biconnected, merely connected, or not required to be connected; and (4) G has at most ℓ1 (respectively, ℓ2) distinct node (respectively, edge) labels. These examples are novel applications of small cycle separators of planar graphs and settle several problems that have been open since Tutte’s census series were published in 1960’s.
optimal encoding
fast methodology
doi
10.1007/3-540-48481-7_47
Springer Nature - SN SciGraph project
Pure Mathematics
Springer Nature
Department of Computer Science and Engineering, State University of New York at Buffalo, 14260, Buffalo, NY, USA
Department of Computer Science and Engineering, State University of New York at Buffalo, 14260, Buffalo, NY, USA
Ming-Yang
Kao
dimensions_id
pub.1006627258
Mathematical Sciences
978-3-540-48481-3
978-3-540-66251-8
Algorithms - ESA’ 99
Lu
Hsueh-I
Jaroslav
Nešetřil
He
Xin
Department of Computer Science, Yale University06250, New Haven, CT, USA
Department of Computer Science, Yale University06250, New Haven, CT, USA
Department of Computer Science and Information Engineering, National Chung-Cheng University, 621, Chia-Yi, Taiwan, ROC
Department of Computer Science and Information Engineering, National Chung-Cheng University, 621, Chia-Yi, Taiwan, ROC