Reading
Lecture Notes
[Eri] J. Erickson. CPS473G: Algorithms. UIUC.
[Goe] M.. Goemans. 18.438: Advanced Algorithms. MIT, 2008.
Linear Programming
- [BTM] S. Bradley, A. Hax, T. Magnanti Duality in Linear Programming, Applied Mathematical Programming(1977), chapter 4.
- [BV] S. Boyd, L. Vandenberghe, Convex Optimization (2004), chapter 5.
- [Dan] G. B. Dantzig, Linear programming, Operations Research 50 (2002), 42-47.
- [GW1] M.X. Goemans and D.P. Williamson, The primal-dual method
for approximation algorithms and its application to network
design problems, in Approximation Algorithms, D. Hochbaum, Ed., 1997.
pdf
- [PS] C. Papdimitrious and K. Steiglitz, Combinatorial Optimization, Prentice Hall, 1982.
- [Sch] A. Schrijver, Theory of Linear and Integer Programing, Wiley Interscience, 1986.
- [Tod] M.J. Todd, The many facets of linear programming, Mathematical Programming 91: 417-436 (2002).
Network Optimization
- [CKM+] P. Christiano, J.A. Kelner, A. Madry, D.A. Spielman, S.-H. Teng: Electrical flows, Laplacian systems, and faster approximation of maximum flow in undirected graphs. Proc. 43rd ACM Symposium on Theory of Computing, 2011, 273-282.
- [HK] John E. Hopcroft, Richard M. Karp: An n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs. SIAM J. Comput. 2(4): 225-231 (1973).
- [Kuh] Harold W. Kuhn: The Hungarian Method for the Assignment Problem. 50 Years of Integer Programming 2010: 29-47.
- [ST] D.D. Sleator and R.E Tarjan, A Data Structure for Dynamic Trees, J. Comp. SYst. Sci., 26 (1983), 114-122.
- [Spi] D. Spielman, Spectral Graph Theory & Its Applications.
- [Tar] R.E. Tarjan, Data Structures and Network Algorithms, SIAM, 1983.
Intractability
- [AB] S. Arora and B. Barak, Computational Complexity, Cambridge, 2009.
- [Eri] J. Erickson, CPS473G: Algorithms, UIUC, chapter 30.
- [GJ] M. Garey and D.S. Johnson, Computers and Intractability, Freeman, 1979.
Approximation Algorithms
Geometry
- [Ai] A. Andoni, P. Indyk: Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. Commun. ACM 51(1): 117-122 (2008).
- [dBCKO] M. de Berg, O. Cheong, M. van Kreveld, and M. Overmars, Computational Geometry: Algorithms and Applications. Springer-Verlag, 3rd ed., 2008.
- [GIW] A. Gionis, P. Indyk, R. Motwani: Similarity Search in High Dimensions via Hashing. VLDB 1999: 518-529.
- [Mat] J. Matousek, Lectures on Discrete Geometry, Springer, 2002.
Hashing
- [AI] A. Andoni, P. Indyk: Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. Commun. ACM 51(1): 117-122 (2008)I
- [HP] S. Har-Peled, Geometric Approximation Algorithms , AMS, 2011
- [CM] Graham Cormode, S. Muthukrishnan:
An improved data stream summary: the count-min sketch and its applications. J. Algorithms 55(1): 58-75 (2005)
- [CGHJ] Graham Cormode, Minos N. Garofalakis, Peter J. Haas, Chris Jermaine:
Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches. Foundations and Trends in Databases 4(1-3): 1-294 (2012)
- [Mu] S. Muthukrishnan, Data Streams: Algorithms and Applications, Foundations and Trends in Computer Science, Now Publishers Inc, 2005.
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