Introduction

In

this term paper will explain a most common problem called Hiring Problem.

Hiring Problem have a huge variety of different problems that can be solved by

using Hiring Problem algorithm. By using different algorithm for hiring tree to

solve many problems like secretary problem or marriage problem. In this term

paper we will discuss the randomized algorithm and probabilistic analysis of a

problem by using this will also discuss other problem as hiring problem. We

will explain some algorithm to solve the hiring problems.

How to define Hiring Problem

Hiring

problem is such a problem in which a company hire a best candidate with the

help of employment agency, the agency sends you a one candidate each day. And

our duty is that to interview the candidate and decide the candidate is

suitable for the company or not. And at each interview we need to hire a best

candidate from the available list to fire the fire previous one. Our main

Purpose is that to calculate or estimate the hiring cost of a best candidate

towards the employment agency.

Algorithms for Hiring Problem

There

is different algorithm to solve the Hiring Problem. But the most common and

standard algorithm to solve the hiring problem is randomized algorithm. A

randomized algorithm is one that receives, in addition to its input data, a

stream of random bits that it can use for making random choices. By using this

we can analysis the best , average and worst case of hiring through which will

hire a such a candidate who have higher best probability according to interview

standards.

Advantages

There

are some advantages toward the Randomized algoritm.

Efficiency:

For

the repeated element identification and primary testing grabs the most effective

part with countless results.

Simplicity:

A

majority of the randomized algorithm found in the literature are simpler than

best deterministic algorithm for the same problem.

Complexity:

This algorithm shows the better complexity bounds. This

algorithm is also easy to practice.

Drawbacks

Time:

This type of

algorithm works in the loop and due to repeatation of the several process it

take the many time slots.

Hardware:

By continuous running

this type of algorithm we face hardware failure problem.

Space:

As the algorithm

works the different process as many time again and again then it requires a

large storage space.

PacMan Game is the

best example of this algorithm and also face these limitations of algorithms.

Applications

These are the few

applications of randomized algorithm.

The Birthday Paradox:

Our ?rst

example is the birthday paradox. How many people must there be in a room before

there is a 50% chance that two of them were born on the same day of the year?

The answer is surprisingly few. According to a

analysis a random group of just 23 people there is about a 50–50 chance that

two of them will have the same birthday. This is known as the birthday paradox.

Balls AND PINS:

Consider a process in which we randomly toss identical balls into b

bins, numbered 1; 2;;;;;;;b. The tosses are independent, and on each toss the

ball is equally likely to end up in any bin. The probability that a tossed ball

lands in any given bin is 1/b. Thus, the ball-tossing process is a sequence of

Bernoulli trials with a probability 1/b of success, where success means that

the ball falls in the given bin. This model is particularly useful for

analyzing hashing and we can answer a variety of interesting questions about

the ball-tossing process.

Streaks:

Suppose you ?ip a fair coin n times. What is the longest streak of

consecutive heads that you expect to see? The answer is ‚Theta( lg n ), and it

can be shown by this algorithm.