Theoretical and Experimental DNA Computation (Natural ...

k=red
For each edge {j,k}
In parallel
remove from
T
T
copy
T T
r
g
remove from T
r
j=green, j=blue
3.2 Filtering Models 53
For j=1 to n do
T
b
remove from T
g
remove from T
b
j=red, j=blue j=red, j=green
For each edge {j,k} For each edge {j,k}
In parallel
In parallel
remove from remove from
T
g
k=green T
b
k=blue
union
select
Fig. 3.1. 3-coloring algorithm flowchart
Solution:
• Input: The input set U is the set Pn of all permutations of the integers
from 1 to n as output from Problem: Permutations. An integer i at
position pk in such a permutation is interpreted as follows: the string represents
a candidate solution to the problem in which vertex i is visited at
step k.
• Algorithm:
for 2 ≤ i ≤ n−1 andj, k such that (j, k) /∈ E
in parallel do remove (U, {jpik})
select(U)
• Complexity: Constant parallel time given Pn.