Dynamic programming determines the optimum solution of a multivariable problem by decomposing it into stages, each stage is comprising of a single variable sub problem. The advantage of the decomposition is that the optimization process at each stage involves one variable only, a simpler task computationally then dealing with all the variables simultaneously. A dynamic programming model is basically a recursive equation linking the different stages of the problem in a manner that guarantees that each stage’s optimal feasible solution is also optimal and feasible for entire problem. Analysis of biological networks is one of the central research topics in computational systems biology. A Bayesian network is a graphbased model of joint multivariate probability distributions that captures properties of conditional independence between variables. Such models are attractive for their ability to describe complex stochastic processes and because they provide a clear methodology for learning from (noisy) observations. We start by showing how Bayesian networks can describe interactions between genes. Suppose that the given set of gens
Network completion is, given an initial network and an observed dataset, to modify the network by the minimum amount of modifications so that the resulting network is (most) consistent with the observed data. Since we were interested in inference of signaling networks in our previous study
In this study, we survey the various methods/techniques available to solve traveling salesman problem and analyze arrow drawing method to make critical evaluation their time complexities. Recursive equation and arrow drawing methods are the methods used to determine the shortest distance in salesman of dynamic programming problem.
The purpose of network completion is to modify a given network with the minimum number of modifications so that the resulting network is most consistent with the observed data. In this paper, we consider additions and creation of sequence in states through stages as modification operations. To find the path of minimum distance between the point of source to terminal using back ward recursion or forward recursion of dynamic programming can be obtained using the following method.
Assign the initial value of the salesman as zero. i.e the value of the stage
let
Starting at i = 1 the recursion sets
The equation shows that the shortest distances
A salesman located in a city A decides to travel city J. He knew the distances of alternative routes from city A to city J, then he drew a high way network map as shown in the figure below. The city of origin is A and the destination city is J. Other cities through which the salesman will have to pass through are named B to I. The arrow is representing routes between cities and distances in kilometers are indicated on each route. The salesman problem is to find shortest route from A to J. Use dynamic programming to solve it.
In the figure above the circular regions are cities and a numbers in the arrows are distance between the cities in kilometer.
The back ward recursive equation is
Stage :4

d( 
Optimal solution 




H 
7+0 
7 
J 
I 
9+0 
9 
J 
Stage :3

d( 
Optimal solution 






E 
7+4=11 8+9=17 
11 
H 


F 
7+3=10 7+9=16 
10 
H 


G 
7+8=15 
13 
I 
Stage:2

d( 
Optimal solution 




B 
11+7=18 10+10=20 13+5=18 
18 
E,G 
C 
11+3=14 10+8=18 13+4=17 
14 
E 
D 
11+6=17 10+10=20 13+5=18 
17 
E 
Stage :1

d( 
Optimal solution 




A 
18+4=22 14+6=20 17+3=20 
20 
C,D 
Therefore, the minimum distance is 20. i.e 
When using arrow drawing method we can determine the shortest and longest paths in each stages but our target is to get the shortest path. Arrow drawing method is simple and short time taking to solve the dynamic programming problem compared to recursive equation. When we apply the forward or backward recursive equation method for the given dynamic programming problem of salesman route, we lose time and complicate to construct the table to find optimal solution.
Hence
Example1. A salesman located in a city A decides to travel city J. He knew the distances of alternative routes from city A to city J, then he drew a high way network map as shown in the figure below. The city of origin is A and the destination city is J. Other cities through which the salesman will have to pass through are named B to I. The arrow is representing routes between cities and distances in kilometers are indicated on each route. The salesman problem is to find shortest route from A to J. Use dynamic programming to solve it.
There fore
A
The value of certain dynamic shortest route among the cities from A to J is 20. The recursive procedure described four different tables which is taken at least 23 lines, time taking and complex to achieve solution but as we have seen the modified method cover 19 lines, time saving and simpler even if we compared in line coverage, time and the way of solving so here was carried out from A to J. Those the same procedure is often utilized in the reverse direction from J to A which leads to an equivalent solution by backward recursion. Hence using arrow drawing method to computing the shortest and longest path between two given location in salesman problem is an important and simplest way that to find applications in various map services. An implementation of the traveling salesman problem using dynamic programming is presented in this paper which generates optimal answer. So these forward and backward recursive methods take time and complex to find optimal solution but
To solve the traveling salesman route we apply the recursive equation (either forward or backward recursive). It is taking long time and very complicate if a number of states are many to get the shortest distance of salesman problem in dynamic programming problem. So that it is better to apply arrow draw method to determine the shortest distance and to take short time for solving the given problem compared to recursive equation. We can see not only the shortest distance of route but also able to identify the longest distance that helps us not to use this longest one to minimize the cost.