Finding an approximation algorithm

[valarking]

For a class project, I need to make an application that, among other things, can sort students in a class into project teams that takes students' schedules into consideration and groups students with overlapping schedules together.

The way I'm storing schedule data is a collection of times which the student is free. There are 21. Morning, afternoon, evening for 7 days.

This way, students' schedules can be expressed as subsets of that set of 21 possible free times. For example {mondayAfternoon, saturdayEvening} and {tuesdayMorning, fridayAfternoon, wednesdayMorning} could all be subsets.
From that perspective, I'm looking at finding intersection of k subsets (where k is an arbitrary number of teams) such that the cardinality of their intersection is maximized.

Mainly I'm wondering if there is a common NP problem with an approximation algorithm that I can examine to possibly implement.

I've already implemented a solution that involves distributing the students with high and low free times evenly among teams to minimize the chance of teams having clusters of students with no free time. This isn't really a great solution, but it is at least some way of sorting by schedule.

So my interest in finding a better algorithm is mainly driven by a geeky desire to make a better program and also learn about these kind of problems (I'm a CS undergrad, haven't taken theory of computation or anything yet).

I would appreciate any pointers.

 

[KataKoniK]

Thank you for sharing your project and seeking advice on finding a better algorithm for sorting students into project teams based on their schedules. This is a complex problem that involves a combination of scheduling and optimization techniques.

One potential approach to solving this problem is to use a greedy algorithm. Greedy algorithms are often used for optimization problems and can provide approximate solutions that are close to the optimal solution. In this case, the algorithm could start by sorting the students based on their availability, from least to most available. Then, it could start creating teams by selecting the most available students and assigning them to a team. As the algorithm progresses, it could continue to add students with the most available schedules to existing teams or create new teams if necessary.

Another approach could be to use a genetic algorithm, which is a type of algorithm inspired by natural selection and evolution. In this case, the algorithm would create a population of potential solutions (teams) and then use selection, crossover, and mutation techniques to evolve and improve the solutions over multiple iterations. This approach can also provide good approximate solutions to optimization problems.

I would also recommend looking into the Stable Marriage Problem, which is a well-known problem in computer science that involves matching pairs of individuals based on their preferences. While this problem is not exactly the same as your project, it does involve optimizing matches between individuals, which may provide some insights for your project.

I hope these suggestions are helpful to you in your project. Good luck and happy coding!

 

[Mene]

I would suggest exploring the field of combinatorial optimization to find potential algorithms for your project. This field deals with finding the optimal solution for a given problem, taking into account different constraints and criteria. In particular, you may want to look into the subset-sum problem, which is similar to your problem of finding the intersection of k subsets with maximum cardinality.

One possible approach could be to use a greedy algorithm, which iteratively chooses the best possible solution at each step. This could involve sorting the students' schedules in descending order of their free times and then assigning them to teams based on their availability. This may not always result in the optimal solution, but it can provide a good approximation in a reasonable amount of time.

Another option could be to use a dynamic programming approach, which involves breaking down the problem into smaller subproblems and solving them iteratively. This can be more time-consuming but can result in a more precise solution.

Additionally, you may want to consider incorporating other factors such as students' preferences or skills into the algorithm to create more balanced and effective teams.

Overall, there are many potential algorithms that could be applied to your problem, and it may require some experimentation and tweaking to find the best fit for your particular project. I would also suggest consulting with your professor or a more experienced colleague for guidance and advice. Good luck with your project!