6.854J | Fall 2008 | Graduate

Advanced Algorithms


There is no textbook required for the course. Lecture notes are available for the current term as well as selected lecture notes from a previous term. Reference textbooks for each topic are listed in the table below.  Lecture notes also contain references.

Network flows Ahuja, R. K., T. L. Magnanti, and J. B. Orlin. Network Flows: Theory, Algorithms, and Applications. Upper Saddle River, NJ: Prentice Hall, 1993. ISBN: 9780136175490.
Data structures

For both splay trees and dynamic trees:

Sleator, and Tarjan. “Self-adjusting Binary Search Trees.” Journal of the ACM 32, no. 3 (July, 1985): 652-686. ISSN: 0004-5411.

Buy at MIT Press  Cormen, T.H., C.E. Leiserson, R.L. Rivest, and C. Stein. Introduction to Algorithms. 2nd ed. Cambridge, MA: MIT Press, 2001. ISBN: 9780262032933.

Linear programming

Schrijver, A. Theory of Linear and Integer Programming. New York, NY: John Wiley & Sons, 1998. ISBN: 9780471982326.

For the Ellipsoid, 3 references are:

Groetschel, M., L. Lovasz, and A. Schrijver. Geometric Algorithms and Combinatorial Optimization. New York, NY: Springer-Verlag, 1993, chapter 3. ISBN: 9780387567402. [The standard reference on the ellipsoid. The most complete and precise description.]

Chvatal, V. Linear Programming. New York, NY: W.H. Freeman and Company, 1983, appendix. ISBN: 9780716715870. [An easy to read description without all the details.]

Korte, B. H., and J. Vygen. Combinatorial Optimization. New York, NY: Springer-Verlag, 2002, chapter 4. ISBN: 9783540431541. [A detailed description.]

For Interior-point Algorithms, a good reference is:

Roos, C., T. Terlaky, and J.-Ph. Vial. Theory and Algorithms for Linear Optimization: An Interior Point Approach. New York, NY: John Wiley & Sons, 1997. ISBN: 9780471956761.

Convex programming

 Boyd, Stephen, and Lieven Vandenberghe. Convex Optimization . Cambridge, UK: Cambridge Univ. Press, 2005. ISBN: 9780521833783

Nemirovski, Arkadi. “Lectures on Modern Convex Optimization.” (PDF - 2.7 MB)

Approximation algorithms

Vazirani, V. Approximation Algorithms. New York, NY: Springer-Verlag, 2004. ISBN: 9783540653677.

Hochbaum, D., ed. Approximation Algorithms for NP-Hard Problems. Boston: PWS Publishing Company, 1996. ISBN: 9780534949686.

Arora, Sanjeev. “Polynomial Time Approximation Schemes for Euclidean Traveling Salesman and Other Geometric Problems.” Journal of the ACM 45, no. 5 (September, 1998). New York, NY, USA: ACM Press. ISSN: 0004-5411.

Geometric algorithms

 de Berg, Mark, O. Cheong, M. van Kreveld, and M. Overmars. Computational Geometry. 3rd ed. New York, NY: Springer-Verlag, 2008.  ISBN: 9783540779735

Streaming algorithms

S. Muthukrishnan, “Data streams: Algorithms and applications”, Foundations and Trends in Theoretical Computer Science, Volume 1, issue 2, 2005.

Number-theoretic algorithms

Lov’asz, L. “An Algorithmic Theory of Numbers, Graphs, and Convexity.” In CBMS Regional Conference Series in Applied Mathematics (SIAM, 1986). Philadelphia, PA: Society for Industrial and Applied Mathematics, 1987. ISBN: 9780898712032.

Buy at MIT Press Bach, E., and J. Shallit. Algorithmic Number Theory. Vol. 1. Cambridge, MA: MIT Press, August 26, 1996. ISBN: 9780262024051.

Course Info

As Taught In
Fall 2008
Learning Resource Types
Lecture Notes
Problem Sets with Solutions