scholarly journals Uniform random sampling of planar graphs in linear time

2009 ◽  
Vol 35 (4) ◽  
pp. 464-522 ◽  
Author(s):  
Éric Fusy
Keyword(s):  
Random Sampling ◽  
Planar Graphs ◽  
Linear Time ◽  
Uniform Random Sampling

scholarly journals A Quantitative Study of Pure Parallel Processes

10.37236/3977 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
O. Bodini ◽  
A. Genitrini ◽  
F. Peschanski
Keyword(s):  
Quantitative Study ◽  
Random Sampling ◽  
Linear Time ◽  
Time Algorithm ◽  
Point Of View ◽  
Total Size ◽  
Combinatorial Explosion ◽  
Analytic Combinatorics ◽  
Parallel Processes ◽  
Uniform Random Sampling

In this paper, we study the interleaving – or pure merge – operator that most often characterizes parallelism in concurrency theory. This operator is a principal cause of the so-called combinatorial explosion that makes the analysis of process behaviours e.g. by model-checking, very hard – at least from the point of view of computational complexity. The originality of our approach is to study this combinatorial explosion phenomenon on average, relying on advanced analytic combinatorics techniques. We study various measures that contribute to a better understanding of the process behaviours represented as plane rooted trees: the number of runs (corresponding to the width of the trees), the expected total size of the trees as well as their overall shape. Two practical outcomes of our quantitative study are also presented: (1) a linear-time algorithm to compute the probability of a concurrent run prefix, and (2) an efficient algorithm for uniform random sampling of concurrent runs. These provide interesting responses to the combinatorial explosion problem.

scholarly journals Linear-Time Succinct Encodings of Planar Graphs via Canonical Orderings

1999 ◽  
Vol 12 (3) ◽  
pp. 317-325 ◽  
Author(s):  
Xin He ◽  
Ming-Yang Kao ◽  
Hsueh-I Lu
Keyword(s):  
Planar Graphs ◽  
Linear Time

scholarly journals Recognizing Outer 1-Planar Graphs in Linear Time

2013 ◽  
pp. 107-118 ◽  
Author(s):  
Christopher Auer ◽  
Christian Bachmaier ◽  
Franz J. Brandenburg ◽  
Andreas Gleißner ◽  
Kathrin Hanauer ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Linear Time
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