In this model a single process can have multiple, concurrent execution paths. The main program is scheduled to run by the native operating system. It loads and acquires all the necessary softwares and user resources to activate the process. Any thread can execute any one subroutine and at the same time it can execute other subroutine.

By sacrificing completeness it increases efficiency. Useful in solving tough problems which could not be solved any other way. Otherwise repeat from 1. This method is basically a depth first search as complete solutions must be created before testing.

It is often called the British Museum method as it is like looking for an exhibit at random. A heuristic is needed to sharpen up the search.

Consider the problem of four 6-sided cubes, and each side of the cube is painted in one of four colours. The four cubes are placed next to one another and the problem lies in arranging them so that the four available colours are displayed whichever way the 4 cubes are viewed.

The problem can only be solved if there are at least four sides coloured in each colour and the number of options tested can be reduced using heuristics if the most popular colour is hidden by the adjacent cube.

This problem is NP-hard and thus interesting. There are a number of algorithms used to find optimal tours, but none are feasible for large instances since they all grow exponentially.

We can get down to polynomial growth if we settle for near optimal tours. We gain speed, speed and speed at the cost of tour quality. So the interesting properties of heuristics for the TSP is mainly speed and closeness to optimal solutions.

There are mainly two ways of finding the optimal length of a TSP instance. The first is to solve it optimally and thus finding the length. The other is to calculate the Held-Karp lower bound, which produces a lower bound to the optimal solution.

This lower bound is the de facto standard when judging the performance of an approximation algorithm for the TSP.

Approximation Solving the TSP optimally takes to long, instead one normally uses approximation algorithms, or heuristics. The difference is approximation algorithms give us a guarantee as to how bad solutions we can get.

Normally specified as c times the optimal value. It is based om geometric partitioning and quad trees. Although theoretically c can be very large, it will have a negative effect on its running time O n log2n O c for two-dimensional problem instances.

Tour Construction Tour construction algorithms have one thing in commmon, they stop when a solution is found and never tries to improve it.

The key to this algorithm is to always visit the nearest city.

Nearest Neighbor, O n 2 1. Select a random city. Find the nearest unvisited city and go there. Are there any unvisitied cities left?MCA Programme Coordinator Visveswarayya Bhawan, C-Block, New Academic Complex, Maidan Garhi New Delhi - Indira Gandhi National Open University Phone: and Fax no Email:[email protected] 5.

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