CMSC 198K: Science behind computing

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CMSC 198K Science behind computing

• Bobby Bhattacharjee
• Samir Khuller
• University of Maryland

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Basic Information

• Syllabus
• Email bobby_at_cs.umd.edu (Bobby)
• Email samir_at_cs.umd.edu (Samir)
• TA Kristin Stephens, ksteph_at_cs.umd.edu
• UTA Hailey Lin, halin2007_at_gmail.com

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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.

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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.

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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.

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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

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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 dont 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.

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

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

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

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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

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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!

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Applications of Algorithms

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

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

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A disclaimer

• I have chosen a set of problems whose algorithms
  are quite simple.
• Towards the end of the talk I will also mention
  some recent projects that are a little more
  involved, and its hard to really describe the
  algorithms and methods used since they are quite
  complex.

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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)

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Mens preference lists
Brad (B)
Vince(V)
2
3
1
George(G)
Jennifer(J)
Laura(L)
Angelina(A)
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Womens Preference List
Jennifer(J)
Angelina(A)
1
2
3
Laura(L)
George(G)
Vince(V)
Brad(B)
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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?

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Unstable Pairing

• Consider the following pairing
• NOTE Angelina prefers Brad to Vince, but Brad
  still prefers Jen to Angelina.

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

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Running the Algorithm
FIRST ROUND Brad proposes to Jen Vince proposes
to Laura George proposes to Jen
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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)
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SECOND ROUND George proposes to Laura
Laura breaks engagement with Vince, and gets
engaged to George (Brad,Jen) and (George,Laura)
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THIRD ROUND Vince proposes to Jen
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THIRD ROUND Vince proposes to Jen
Jen breaks engagement with Brad, and gets engaged
to Vince (Vince,Jen) and (George,Laura)
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FOURTH ROUND Brad proposes to Angelina
Angelina accepts and gets engaged to
Brad (Vince,Jen), (George,Laura) and
(Brad,Angelina)
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The couples