Grid Graph Reachability Problems

2006 ◽  
Author(s):  
E. Allender ◽  
D.A. Mix Barrington ◽  
T. Chakraborty ◽  
S. Datta ◽  
S. Roy
Keyword(s):  
Grid Graph ◽  
Graph Reachability

Planar and Grid Graph Reachability Problems

2009 ◽  
Vol 45 (4) ◽  
pp. 675-723 ◽  
Author(s):  
Eric Allender ◽  
David A. Mix Barrington ◽  
Tanmoy Chakraborty ◽  
Samir Datta ◽  
Sambuddha Roy
Keyword(s):  
Grid Graph ◽  
Graph Reachability

scholarly journals Maximal independent sets on a grid graph

2017 ◽  
Vol 340 (12) ◽  
pp. 2762-2768 ◽  
Author(s):  
Seungsang Oh
Keyword(s):  
Independent Sets ◽  
Grid Graph ◽  
Maximal Independent Sets

Grid graph planning and control method applied to equipment maintenance in the chemical industry

1967 ◽  
Vol 3 (3) ◽  
pp. 231-234 ◽  
Author(s):  
E. K. Sashina ◽  
�. I. Shklovskii ◽  
A. B. Miller ◽  
Yu. S. Chentsov
Keyword(s):  
Chemical Industry ◽  
Control Method ◽  
Equipment Maintenance ◽  
Grid Graph ◽  
Planning And Control ◽  
And Control ◽  
Graph Planning

scholarly journals A Probabilistic Analysis of a String Editing Problem and its Variations

1995 ◽  
Vol 4 (2) ◽  
pp. 143-166 ◽  
Author(s):  
Guy Louchard ◽  
Wojciech Szpankowski
Keyword(s):  
Generating Functions ◽  
Edit Distance ◽  
Optimal Path ◽  
Minimum Cost ◽  
Probabilistic Framework ◽  
Grid Graph ◽  
Average Value ◽  
Typical Behaviour ◽  
Maximum Minimum ◽  
Independent Model

We consider a string editing problem in a probabilistic framework. This problem is of considerable interest to many facets of science, most notably molecular biology and computer science. A string editing transforms one string into another by performing a series of weighted edit operations of overall maximum (minimum) cost. The problem is equivalent to finding an optimal path in a weighted grid graph. In this paper we provide several results regarding a typical behaviour of such a path. In particular, we observe that the optimal path (i.e. edit distance) is almost surely (a.s.) equal to αn for large n where α is a constant and n is the sum of lengths of both strings. More importantly, we show that the edit distance is well concentrated around its average value. In the so called independent model in which all weights (in the associated grid graph) are statistically independent, we derive some bounds for the constant α. As a by-product of our results, we also present a precise estimate of the number of alignments between two strings. To prove these findings we use techniques of random walks, diffusion limiting processes, generating functions, and the method of bounded difference.

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