CMSC 198K: Science behind computing

1. CMSC 198K: Science behind computing Bobby Bhattacharjee Samir Khuller University of Maryland

2. Basic Information • Syllabus • Email: bobby@cs.umd.edu (Bobby) • Email: samir@cs.umd.edu (Samir) • TA – Kristin Stephens, ksteph@cs.umd.edu • UTA – Hailey Lin, halin2007@gmail.com

3. Course Web Page • http://www.cs.umd.edu/class/fall2009/cmsc198k/ • All course materials (lecture notes, handouts, homeworks) shall be available on the class page. • Dates for the exams shall be announced shortly.

4. Computer Science • What is the computer actually doing? • Its running a program (a set of instructions), but what is the program doing? • Typically, an algorithm is what the program implements.

5. Science vs Technology • We are all familiar with the technology, the internet, the web, the ability to access information, videos, news, make reservations, email – we use this everyday. • How did this happen? • Computer Science is a very young field, with most of the innovation having happened in just the last 60 years.

6. Outline of Topics • Elementary Algorithms • Basics about computers • Basics about programming • Concepts/Computational thinking • Some elementary mathematics • The fun stuff: Internet/Secret message sharing/Communication/Randomization

7. A typical conversation Person: What do you do? Me: I am a computer science professor. Person: I have a problem with my PC, can you fix it? Me: No, I don’t think I can do that. Person: You will not fix my PC? Me: I cannot fix my PC, let alone yours. Person: Then what exactly do you do? Me: I study algorithms. Person: Oh, I know that. Me: Really? Person: Yes! I learnt logarithms in high school.

8. Algorithms not Logarithms! L O G A R I T H M Al-Khowarizmi

9. Algorithms Introduction Recipe for baking a cake…. • 2 sticks butter • 2 cups flour • 1 cup sugar • 4 eggs • 1 cup milk • 1 tsp baking powder • Cocoa powder (1/2 pound) Mix the sugar, baking powder and flour, mix in beaten eggs, melted butter and bake at 325F for 40 mins.

10. ALGORITHMS • Set of instructions for solving a problem, to find a solution. • What is a problem? • What is an instruction? • What is a solution?

12. Why are algorithms central to computing? • An airport shuttle company needs to schedule pickups delivering everyone to the airport on time. Who goes in which shuttle, and in what order do the pickups occur? • A delivery company has several customers and trucks that can carry objects. How should they schedule deliveries to the customers to minimize their cost? This leads to interesting algorithmic problems…

13. There are lots of feasible solutions! • How should we pick amongst these solutions? • Some solutions are cheap, and others may be expensive or undesirable. • The number of potential solutions is so large that even a fast computer cannot evaluate all these solutions. • Algorithms tell us how to find good solutions!

14. Applications of Algorithms • Google News • Web Search applications • Find a file on your computer • Assigning people to tasks • E-harmony • Resident Assignment Problems

15. Re-assigning employees A A B B C C D D

16. Assigning Interns to Hospitals • The “resident matching” program is a computer program that assigns residents (interns) to hospitals. • Also used for admission to High Schools in several Asian countries. • Many metrics can be defined, we focus on a specific metric here.

17. The Marriage Problem • N men, N women • Each person provides a ranking of the members of the opposite sex • Can we find a “good marriage”? • First studied by Gale and Shapley (1962)

18. Men’s preference lists Brad (B) Vince(V) 2 3 1 George(G) Jennifer(J) Laura(L) Angelina(A)

19. Women’s Preference List Jennifer(J) Angelina(A) 1 2 3 Laura(L) George(G) Vince(V) Brad(B)

20. Stable Marriage Problem • A marriage is unstable if there is a pair of people, not married to each other, such that both prefer each other to their current partners. In other words, they have an incentive to elope…. • Can we find a “stable” marriage?

21. (Brad, Jen) (Vince, Angelina) (George, Laura) Unstable since Jen and Vince both prefer each other to their current partners.

22. An application: resident matching program • Each resident rank orders the hospitals, and each hospital rank orders the residents. • How do we choose an assignment of residents to hospitals? • We do not want a situation that a resident prefers another hospital, and that hospital preferred this resident to the person assigned to them.

23. FIRST ROUND: Brad proposes to Jen Vince proposes to Laura George proposes to Jen Jen rejects George, engaged to Brad Laura engaged to Vince Angelina gets no proposals…. (Brad,Jen) and (Vince, Laura)

24. SECOND ROUND: George proposes to Laura Laura breaks engagement with Vince, and gets engaged to George (Brad,Jen) and (George,Laura)

25. THIRD ROUND: Vince proposes to Jen

26. THIRD ROUND: Vince proposes to Jen Jen breaks engagement with Brad, and gets engaged to Vince (Vince,Jen) and (George,Laura)

27. FOURTH ROUND: Brad proposes to Angelina Angelina accepts and gets engaged to Brad (Vince,Jen), (George,Laura) and (Brad,Angelina)

28. The couples