You are organizing a big dinner party for your company retreat. To increase social interaction among the various departments in your company, you would like to set up a seating arrangement so that no...

Extracted text: You are organizing a big dinner party for your company retreat. To increase social interaction among the various departments in your company, you would like to set up a seating arrangement so that no two members of the same departments are at the same table. Show how to formulate the problem of finding a seating arrangement that meets this objective as a maximum flow problem. Assume that the company has n departments, and the ith department has m; members. Also assume that t tables are available and the jth table has a seating capacity of c. Provide a step by step algorithm for this problem for maximizing the flow and analyze its running time.