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Course : Algorithms and Applications (15-499) Instructor : Guy Blelloch TA : Shuchi Chawla PowerPoint PPT Presentation


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Course : Algorithms and Applications (15-499) Instructor : Guy Blelloch TA : Shuchi Chawla URL : www.cs.cmu.edu/~guyb/realworld/indexS03.html. Expected Background. Asymptotic analysis (solving recurrences, NP-complete problems)

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Course : Algorithms and Applications (15-499) Instructor : Guy Blelloch TA : Shuchi Chawla

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Course algorithms and applications 15 499 instructor guy blelloch ta shuchi chawla

  • Course:Algorithms and Applications (15-499)

  • Instructor: Guy Blelloch

  • TA: Shuchi Chawla

  • URL: www.cs.cmu.edu/~guyb/realworld/indexS03.html

15-499


Expected background

Expected Background

  • Asymptotic analysis (solving recurrences, NP-complete problems)

  • Graph Terminology and Algorithms (e.g. min-spanning-tree and max-flow algorithms)

  • Dynamic programming

  • Matrix algebra (e.g. null-spaces, eigenvalues)

  • Fast Fourier Transform

  • Probability

15-499


Course requirements

Course Requirements

  • Readings

    • Chapters, papers, course-notes, web documents

    • There is NO course textbook

  • Assignments

    • 6 written assignments (must hand them in individually)

  • Project

    • Group programming project due at the end of the semester. Groups of 2 or 3.

  • Midterm and Final

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Why care about algorithms

Why care about algorithms?

  • Just about every field uses algorithms

    • Engineering, Physical sciences, Social sciences

    • Business, Medicine

    • Probably used more widely than Calculus

  • The level of sophistication has increased significantly in recent years

  • Asymptotics becoming more important

    • Linear programming (interior-point methods)

    • Factoring (number-field sieve)

Some Examples

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Standard complaints about algorithm analysis

Standard complaints about algorithm analysis

  • Irrelevant problem

  • Impractical constants hidden in big-O

  • Bad machine models

  • Too complicated

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On strassen s matrix multiply

On Strassen’s Matrix Multiply

  • From Numerical Recipes (Press et. al. 1986)

    “We close the chapter with a little entertainment, a bit of algorithmic pretidigitation

  • and later in the same section

    “This is fun, but let’s look at practicabilities: If you estimate how large N has to be before the difference between exponent 3 and exponent 2.807 is substatial enough to outweigh the bookkeeping overhead, arising from eht compicated nature of the recursive Strassen algorithm, you will find that LU decomposition is in no immediate danger of coming obsolete.”

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From an experimental paper

From an Experimental Paper

  • From an experimental paper (Bailey, Lee and Simon):

    “For many years it was thought that [the level at which Strassen’s algorithm is more efficient] was well over 1000x1000. In fact, for some new workstations, such as the Sun-4 and SGI IRIS 4D, Strassen is faster for matrices as small as 16x16.

  • Most modern matrix libraries now supply Strassen as a choice

    • IBM ESSL library

    • Cray Libraries

    • LAPACK library

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Topics

Topics

  • Data Compression (5)

    • gzip, bzip, jpeg, mpeg, …

  • Cryptography (5)

    • ssh, RSA, Rijdael, kerberos, …

  • Error Correcting Codes (3)

    • Reed-Solomon, tornado-codes, CDs

  • Computational Biology (5)

    • Genome sequencing, BLAST, evolutionary trees, …

  • Indexing and Searching (5)

    • Google pagerank, duplicate removal, …

  • (n) = number of lectures (approximate)

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What each topic will cover

What each topic will cover

  • Key problems in the area

    • Formal definitions

    • How they relate to practice

  • Many algorithms

    • Theory

    • Practice

  • Key applications along with case studies

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Some general themes

Some General Themes

  • Measures of “performance” beyond “Time”

    • Quality of results

    • Generality

    • Simplicity

  • Transition from theory to practice

    • Often an iterative process

  • Characterizing input

    • Input data is rarely “worst case” or even “expected case” when the expectation is over all possible inputs.

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For next tuesday

For Next Tuesday

  • Read the readings on Data Compression: http://www.cs.cmu.edu/~guyb/realworld/indexS03.html

  • Start homework 1a.

15-499


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