https://github.com/sleekpanther/interval-scheduling

Greedy Algorithm to find the maximum number of mutually compatible jobs
https://github.com/sleekpanther/interval-scheduling

algorithm algorithm-design algorithms compatible greed greedy greedy-algorithm greedy-algorithms interval interval-scheduling jobs noah noah-patullo noahpatullo optimal pattullo pattulo patullo patulo schedule

Last synced: 3 months ago
JSON representation

Greedy Algorithm to find the maximum number of mutually compatible jobs

• Host: GitHub
• URL: https://github.com/sleekpanther/interval-scheduling
• Owner: SleekPanther
• Created: 2017-08-05T14:45:59.000Z (almost 8 years ago)
• Default Branch: master
• Last Pushed: 2017-08-07T11:48:26.000Z (almost 8 years ago)
• Last Synced: 2025-01-15T13:08:07.488Z (5 months ago)
• Topics: algorithm, algorithm-design, algorithms, compatible, greed, greedy, greedy-algorithm, greedy-algorithms, interval, interval-scheduling, jobs, noah, noah-patullo, noahpatullo, optimal, pattullo, pattulo, patullo, patulo, schedule
• Language: Java
• Homepage:
• Size: 657 KB
• Stars: 4
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

        
# Interval Scheduling

Greedy Algorithm to find the **maximum number** of mutually compatible jobs

## Problem Statement

- Job j starts at s(j) and finishes at f(j)

- 2 jobs are **compatible** if they do not overlap (2nd job starts after or at the same time as the 1st one finishes)

- **Goal: find the maximum number of mutually compatible jobs**

- Example: 8 jobs {a, b, c, d, e, f, g, h}

![](images/all-jobs.png)

### Optimal = {b, e, h}

![](images/optimal-jobs.png)

## Algorithm

**Consider jobs in ascending order of finish time f(j)**

### Sorted Jobs

![](images/sorted-jobs.png)

### Pseudocode

![](images/pseudocode.png)

## Runtime

Sorting O(n log(n)) + for-loop Θ(n)  

**O(n log(n))**

## References

- [Kevin Wayne Slides](https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pearson/04GreedyAlgorithms-2x2.pdf)

- [University of Washington Slides](https://courses.cs.washington.edu/courses/cse421/07su/slides/04greed-4up.pdf)

- [T. M. Murali Slides](http://courses.cs.vt.edu/cs5114/spring2009/lectures/lecture04-greedy-scheduling.pdf)

- [Carl Kingsford Slides](https://www.cs.umd.edu/class/fall2009/cmsc451/lectures/Lec04-interval.pdf)

- [Violetta lonati Slides](http://lonati.di.unimi.it/algo/0910/lab/kowalski6.pdf)