GATE-CS-2002 Problem 6

Introduction

GATE-CS-2002 Problem 6 is a programming problem that involves solving a scheduling problem, where we need to find a schedule that maximizes the number of tasks completed within a given time frame.

Problem Statement

Consider the problem of scheduling n jobs on m machines. Each job i is represented by a pair of integers (ai, bi), where ai is the time required to process the job on any machine and bi is the deadline by which the job must be completed. A job can be processed on any machine, but each job can be processed on only one machine. The objective is to find a schedule that maximizes the number of jobs completed by their deadline.

Approach

One possible approach to solve this scheduling problem is to use a greedy algorithm. Sort the jobs in decreasing order of their deadlines. Then, for each job i, assign it to the machine that has the minimum processing time among the available machines. If there is no available machine, discard the job.

The pseudocode of the algorithm is as follows:

Sort the jobs in decreasing order of their deadlines
For each job i:
  Find the machine with the minimum processing time among the available machines
  If such a machine exists:
    Assign job i to the machine
  Else:
    Discard job i

Code

Here is an implementation of the above greedy algorithm in Python:

def schedule_jobs(jobs, machines):
    jobs.sort(key=lambda x: x[1], reverse=True)
    schedule = [[] for _ in range(machines)]
    for job in jobs:
        machine = None
        min_time = float('inf')
        for i in range(machines):
            if job[0] <= min_time and len(schedule[i]) < job[1]:
                machine = i
                min_time = job[0]
        if machine is not None:
            schedule[machine].append(job)
    return schedule

Conclusion

In conclusion, GATE-CS-2002 Problem 6 is a scheduling problem that can be solved using a greedy algorithm. The algorithm assigns jobs to machines in a way that maximizes the number of jobs completed by their deadline. The provided implementation in Python serves as an example of how to approach this problem.