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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. 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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  1. Course:Algorithms and Applications (15-499) • Instructor: Guy Blelloch • TA: Shuchi Chawla • URL: www.cs.cmu.edu/~guyb/realworld/indexS03.html 15-499

  2. 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

  3. 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 15-499

  4. 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 15-499

  5. Standard complaints about algorithm analysis • Irrelevant problem • Impractical constants hidden in big-O • Bad machine models • Too complicated 15-499

  6. 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.” 15-499

  7. 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 15-499

  8. 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) 15-499

  9. 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 15-499

  10. 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. 15-499

  11. 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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