CSE 5311 Class Project Bipartite Matching using Network

CSE 5311 -Class Project Bipartite Matching using Network Flow By: Mahesh Gupta(1000746204) Nandish Jayaram(1000728413)

Problem Statement: Given a set of employees and task names which each employee can complete, we have to model this scenario as a Bipartite Graph to allocate work in such a way that maximum number of tasks are finished while also maximizing the number of employees used. This problem has to be solved using Network flow algorithms: Ford-Fulkerson and Edmond-Karp. UI must help the user visualize path during each iteration.

Our Solution: We implemented our solution using Java. Input File format we have chosen is: T 1: E 2, E 1, E 3 T 2: E 2, E 3 T 3: E 3. Path selection algorithm used for Ford-Fulkerson is Depth. First-Search (DFS) and for Edmond Karp is Breadth-First. Search (BFS). • • References: Network Flow Algorithm’s Ford-Fulkerson and Edmond-Karp as described in “Introduction to Algorithms Third Edition “ by Cormen, Leiserson, Rivest & Stein. •

User Interface: Blue lines between task and employee nodes is the answer.

Demo

Performance Analysis: 350000 300000 250000 200000 EK(Time(MS)) FF(Time(MS)) 150000 100000 50000 0 0 200 400 600 800 1000 1200 1400 X-Axis: No. of Task , Y-Axis: Time taken in Milliseconds 1600 1800 2000 2200 2400 2600 2800 3000 3200

Performance Analysis: 90000 80000 70000 60000 50000 EK-Time X-Axis: No. of Task , Y-Axis: Time taken in Milliseconds FF-Time 40000 30000 20000 10000 0 0 0, 1 0, 2 0, 3 0, 4 0, 5 0, 6 0, 7 X-Axis: Probability for creating an edge , Y-Axis: Time taken in Milliseconds 0, 8 0, 9 1

Thank You