Exhaustive search involves systematically enumerating all potential solutions to a problem and checking if each one is a valid solution. It can solve problems that efficient algorithms cannot by simply trying every possibility, though this becomes intractable for large problems. The traveling salesman problem is an example where checking the length of every possible tour route between cities requires exhaustive search for even moderate numbers of cities. While slow, exhaustive search guarantees finding the optimal solution if allowed to run to completion.

1. Exhaustive Search
Kasun Ranga Wijeweera
(Email: krw19870829@gmail.com)

2. Motivation
• Some problems involve searching through a vast number of
potential solutions to find an answer
• They do not seem to be amendable to solution by efficient
algorithms

3. What is an Efficient Algorithm?
• We have become conditioned to thinking that an algorithm
must be linear or run in time proportional to something like N
or N log N
• We generally consider quadratic algorithms are bad and cubic
algorithms are awful
• Even N50 algorithm would be pleasing because these problems
are believed to require exponential time

4. Travelling Salesman Problem
• Given a set of N cities, find the shortest route connecting them
all, with no city visited twice
• It is still unthinkable to solve an arbitrary instance of the
problem for N = 1000
• There seems to be no way to avoid having to check the length
of a very large number of possible tours
• Checking each and every tour is exhaustive search

5. What is Exhaustive Search?
• Also known as Brute Force Search or Generate and Test
Search
• First enumerate all possible candidates for the solution
• Then check whether each candidate satisfies the problem’s
statement

6. Reference

7. Any Questions?

8. Thank You!