Computing the Weighted Isolated Scattering Number of Interval Graphs in Polynomial Time

Algorithm 2

Algorithm weighted isolated scattering number.

Input: An interval graph , as in Algorithm 1; Minimal local cuts , as generated by Algorithm 1.

Output: Weighted Isolated scattering number .

1 begin

2;

3;

4;

5;

6 for   to and for to   do

7compute the vertex set ;

8if    then

9 mark “empty”;

10end

11  if   and is a complete induced subgraph  then

12mark “complete”.

13 end

14For all nonmarked tuples , , check whether is connected;

15 if    is connected  then

16mark “noncomplete” and for every , compute the components

of , .

Check whether is a minimal local cut of , and if so mark “minimal”, store

in a linked list with a pointer from to the head of this list,

and compute .

17 end

18 if   is disconnected  then

19 compute the components ,

, of and store

in a linked list with a pointer from to the head of this list.

20 end

21 For every pair marked “complete”;

22 if  is of order 1  then

23compute the number of such pair .

24 end

25 else if  the order of is greater than 1  then

26compute according to equation (15).

27 for   to and for to   do

28 if is marked “noncomplete” compute

according to equation (16).

29 end

30 end

31 end