Search Algorithms Jennifer Mosher Math 382 Explicitly Stored - - PowerPoint PPT Presentation

Search Algorithms

Jennifer Mosher Math 382

Explicitly Stored Databases

• Bank account information
• Electronic documents
• Personnel data
• Manufacturing databases
• Financial databases
• An example: Quickbooks.

Linear vs Binary Search

• Linear Search
• Goes through an

average of half of the array before it finds match.

• Less Efficient
• Two Situations
• Binary Search
• Goes through, at

most, half of the array before it finds match.

• More Efficient
• Array must be
• rdered
• Three Situations

The Algorithms

• {1, 2, 3, 4, 5}
• Key = 3
• Key is compared to

1, 2, 3…

• Finds a match.
• Returns index, in

this case 2.

• {1, 2, 3, 4 ,5}
• Key = 3
• Key is compared to

middle element 3.

• Key matches.
• Returns index, again

2.

• {1, 2, 3, 4, 5}
• Key = 7
• Key is compared to

1, 2, 3, 4, 5.

• The search does not

find a match.

• Returns -1.
• The search is

finished.

• {1, 2, 3 , 4, 5}
• Key = 7
• Key is compared to

middle element, 3.

• Doesn’t match.
• 7 > 3
• Searches second half
• f array.
• Key compared to 4

and 5.

• No match, returns
• (insertion point + 1) =
• (5 + 1) = -6

Binary Search Tree

• Binary Search Tree uses nodes
• Four Situations

Virtual Search Spaces, Heuristics and Metaheuristics

• Used to solve discrete optimization

problems

• Approximate
• Good solutions in short amount of time
• Usually not optimal solution

The Tabu Search

• Created by Fred Glover, 1986
• Metaheuristic
• Tabu lists

– Short term memory of search – Tabus

• Disallows moves that would undo prior moves
• Sometimes too powerful

– Aspiration Criteria

Termination of Tabu Search

• Most popular ways:

– After a fixed number of iterations – After some number of iterations without improvement in the objective function value – When an object reaches a pre-specified threshold value

Simulated Annealing

• “Annealing”:

– Process of heating and then cooling something repeatedly for softening and making material less brittle.

• Traveling Salesman Problem
• Tricks:

– Allows Bad Trades – Lowering the temperature

• Used for solving Sudoku

Constraint Propagation

• Constraint Satisfaction Problems (CSP)
• Infers that certain values cannot be part of

certain variable domains because they violate some constraint.

• An Example:

– Constraint: y - 2x, 1 < x < 2

– Conclusion: 2 < y < 4 – In other words, y cannot be less than or equal to 2, or greater than or equal to 4.

Combinatorial Search

• Used for CSP-like problems
• Finds combinations of a discrete set of

items that satisfy certain constraints

• Combinatorial Optimization:

– Finds a combination that maximizes or minimizes some parameter.

• Drawback: solution time can grow

exponentially with the problem size.

Quantum Computers

• Today’s computers are limited to two

states: a 0 or a 1.

• Quantum computer is not.

– 0, 1, or superposition of 0 and 1.

• In other words the symbols are both 0

and 1 and all points in between at the same time.

Grover’s Algorithm

• Invented in 1996 by Lov Grover
• Poses following problem:

– There is an unsorted database containing N items out of which just one item satisfies a given condition-- than item has to be retrieved. There does not exist any sorting on the database that would aid its selection.

• Only other way is the Linear Search, which

would use O(N) steps.

• Grover’s Algorithm would use O(Sqrt(N))
• It is a quicker version of the linear search.

The Importance of Search Algorithms

• Integral part of new technology age of

the world.

• Google.com, youTube, spell check,

searching for a song in iTunes, and more.