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To convert an adjacency list model into a nested set model

3 messages · Gesmann, Markus, Gabor Grothendieck, Martin Maechler

#
Dear R-help

I am wondering if somebody wrote some code to convert an adjacency list
model into a nested set model.
In principal I want to do the same as John Celko mentioned it here with
SQL:
http://groups.google.co.uk/groups?hl=en&lr=lang_en&selm=8j0n05%24n31%241
%40nnrp1.deja.com

Assume you have a tree structure like this
    	        Albert 
             /       \
           /           \
         Bert        Chuck 
                   /    |   \
                 /      |     \
               /        |       \
             /          |         \
        Donna        Eddie       Fred

in an adjacency list model:
emp   boss
1 Albert   <NA>
2   Bert Albert
3  Chuck Albert
4  Donna  Chuck
5  Eddie  Chuck
6   Fred  Chuck

Then it is quite hard to find the all the supervisors of one employee.
John's suggestion is to convert the adjacency list model into a nested
set model.
The organizational chart would look like this as a directed graph:

            Albert (1,12)
            /        \
          /            \
    Bert (2,3)    Chuck (4,11)
                   /    |   \
                 /      |     \
               /        |       \
             /          |         \
        Donna (5,6)  Eddie (7,8)  Fred (9,10)

The data is than stored in the following form:
emp lft rgt
1 Albert   1  12
2   Bert   2   3
3  Chuck   4  11
4  Donna   5   6
5  Eddie   7   8
6   Fred   9  10

To find now the supervisor of an employee all you have to do is to look
where the employees lft figure is between lft and rgt. The supervisors
of Eddie are therefore
emp lft rgt
1 Albert   1  12
3  Chuck   4  11

In the site mentioned above John provides also some code to transform a
adjacency list model into a nested set model. 
Does somebody know if there is already a package for this in R? 

Kind Regards

Markus Gesmann



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#
Gesmann, Markus <Markus.Gesmann <at> lloyds.com> writes:

: 
: Dear R-help
: 
: I am wondering if somebody wrote some code to convert an adjacency list
: model into a nested set model.
: In principal I want to do the same as John Celko mentioned it here with
: SQL:
: http://groups.google.co.uk/groups?hl=en&lr=lang_en&selm=8j0n05%24n31%241
: %40nnrp1.deja.com
: 
: Assume you have a tree structure like this
:     	        Albert 
:              /       \
:            /           \
:          Bert        Chuck 
:                    /    |   \
:                  /      |     \
:                /        |       \
:              /          |         \
:         Donna        Eddie       Fred
: 
: in an adjacency list model:
: 
: > emp=c("Albert", "Bert", "Chuck", "Donna", "Eddie", "Fred")
: > boss=c(NA, "Albert", "Albert", "Chuck", "Chuck", "Chuck")
: > print(Personnel<-data.frame(emp, boss))
:      emp   boss
: 1 Albert   <NA>
: 2   Bert Albert
: 3  Chuck Albert
: 4  Donna  Chuck
: 5  Eddie  Chuck
: 6   Fred  Chuck
: 
: Then it is quite hard to find the all the supervisors of one employee.
: John's suggestion is to convert the adjacency list model into a nested
: set model.
: The organizational chart would look like this as a directed graph:
: 
:             Albert (1,12)
:             /        \
:           /            \
:     Bert (2,3)    Chuck (4,11)
:                    /    |   \
:                  /      |     \
:                /        |       \
:              /          |         \
:         Donna (5,6)  Eddie (7,8)  Fred (9,10)
: 
: The data is than stored in the following form:
: 
: > lft=c(1,2,4,5,7,9)
: > rgt=c(12,3,11,6,8,10)
: > print(Per<-data.frame(emp, lft, rgt))
:   emp lft rgt
: 1 Albert   1  12
: 2   Bert   2   3
: 3  Chuck   4  11
: 4  Donna   5   6
: 5  Eddie   7   8
: 6   Fred   9  10
: 
: To find now the supervisor of an employee all you have to do is to look
: where the employees lft figure is between lft and rgt. The supervisors
: of Eddie are therefore
: > subset(Per, lft < 7 & rgt > 7)
:      emp lft rgt
: 1 Albert   1  12
: 3  Chuck   4  11
: 
: In the site mentioned above John provides also some code to transform a
: adjacency list model into a nested set model. 
: Does somebody know if there is already a package for this in R? 
: 
: Kind Regards
: 
: Markus Gesmann
: 

This is not a direct answer to getting a nesting from an adjacency
but the following is easy to do and gives all the same info.


Note that if A is the adjacency matrix of children (rows) and ]
parents (columns) then A^n is the matrix defining ancestors n 
generations away and exp(A) is a weighted version of that with
A^i weighted by i! (These expressions are mathematics, not R.)  
Thus:

empf <- factor(emp, level = union(emp, boss))  # emp as factor
bossf <- factor(boss, level = union(emp, boss)) # ditto for boss

adj <- table(empf, bossf)  # i,j is 1 if j is boss of i

library(rmutil)  # http://popgen.unimaas.nl/~jlindsey/rcode.html
mexp(adj, type = "series") - diag(length(empf))

giving a matrix whose i,j-th entry is 1/n! if j is n-generations above i.
#
<..............>

    Gabor> This is not a direct answer to getting a nesting from
    Gabor> an adjacency but the following is easy to do and
    Gabor> gives all the same info.


    Gabor> Note that if A is the adjacency matrix of children
    Gabor> (rows) and ] parents (columns) then A^n is the matrix
    Gabor> defining ancestors n generations away and exp(A) is a
    Gabor> weighted version of that with A^i weighted by i!
    Gabor> (These expressions are mathematics, not R.)  Thus:

    Gabor> empf <- factor(emp, level = union(emp, boss))  # emp as factor
    Gabor> bossf <- factor(boss, level = union(emp, boss)) # ditto for boss

    Gabor> adj <- table(empf, bossf)  # i,j is 1 if j is boss of i

    Gabor> library(rmutil)  # http://popgen.unimaas.nl/~jlindsey/rcode.html
    Gabor> mexp(adj, type = "series") - diag(length(empf))

just a note on the matrix exponential:

The Matrix package (from CRAN) now also has the matrix
exponential,  expm(.) , 
using the ''least dubious '' algorithm of

  Moler, C. and Van Loan C. (2003)
  "Ninteen dubious ways to compute the exponential of a
   matrix, twenty-five years later".
  SIAM review 45, 3--49

namely the one also in use by Matlab and Octave

So the above would be something like

library(Matrix)
expm( as(adj, "dgeMatrix") ) - as(diag(length(empf)), "dgeMatrix")


    Gabor> giving a matrix whose i,j-th entry is 1/n! if j is
    Gabor> n-generations above i.

    Gabor> From that you can get the info you need.