A fast parallel algorithm for six-colouring of planar graphs

2005 ◽  
pp. 273-282 ◽  
Author(s):  
Krzysztof Diks
Keyword(s):  
Parallel Algorithm ◽  
Planar Graphs

A PARALLEL ALGORITHM FOR MINIMUM DUAL-COVER WITH APPLICATION TO CMOS LAYOUT

1991 ◽  
Vol 01 (02) ◽  
pp. 177-204 ◽  
Author(s):  
Y.M. HUANG ◽  
M. SARRAFZADEH
Keyword(s):  
Parallel Algorithm ◽  
Planar Graphs ◽  
Dual Graph ◽  
Minimum Area ◽  
Minimum Cardinality ◽  
Vlsi Layout ◽  
Model Based ◽  
Pram Model ◽  
Better Than

In a pair of planar graphs (G, Gd), with Gd being the dual graph of G, a sequence of distinct edges is a dual-Euler trail if it is a trail both in G and in Gd. A set of disjoint dual-Euler trails that simultaneously cover G and Gd is called a dual-cover. We present an O( log n) time and O(n) processors algorithm, in PRAM model, based on the graph separator theory, for obtaining a minimum cardinality dual-cover in a pair of series-parallel graphs (G, Gd), where n is the total number of edges. We employ the proposed algorithm to obtain a minimum-area VLSI layout of CMOS functional cells. Our algorithm, when implemented in a serial environment performs better than previous algorithms and produces more compact layouts.

Acute Constraints in Straight-Line Drawings of Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 994-1001
Author(s):  
Akane SETO ◽  
Aleksandar SHURBEVSKI ◽  
Hiroshi NAGAMOCHI ◽  
Peter EADES
Keyword(s):  
Planar Graphs ◽  
Line Drawings ◽  
Straight Line

A Space-Efficient Separator Algorithm for Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 1007-1016 ◽  
Author(s):  
Ryo ASHIDA ◽  
Sebastian KUHNERT ◽  
Osamu WATANABE
Keyword(s):  
Planar Graphs
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