Time and Place: Mondays and Wednesdays, 9-10am, Bell 244

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Computer Science and Engineering

Instructors: Hung Q. Ngo and Atri Rudra.

- [ pdf ] What is Group Testing? Problem formulation, prototypical applications, the matrix representations with disjunct and separable matrices. Four main objectives: (1) reducing number of tests, (2) efficient constructions, (3) efficient decoding, (4) error-tolerance.
- [ pdf ]
Lower bounds on the number of tests.
- M. Ruszinko, On the upper bound of the size of the r-cover-free families, J. Combin. Theory Ser. A, 66 (1994), pp. 302–310. [ pdf ]
- Z. Furedi,
*On r-cover-free families*, Journal of Combinatorial Theory, Ser. A 73 (1996), 172-173. [ pdf ] - P. Erdös, P. Frankl, and Z. Furedi:
*Families of finite sets in which no set is covered by the union of r others*, Israel Journal of Mathematics 51 (1985), 79-89. [ pdf ]

- [ pdf ] Brief introduction to coding theory: codes, Singleton bound, linear codes, Reed-Solomon codes, code concatenation, Gilbert-Varshamov bound.
- [ pdf ]
Probabilistic upper bounds on the number of tests.
The code concatenation technique.
Concatenating a random code with the identity code.
Connection to the k-restriction problem.
- Even, G., Goldreich, O., Luby, M., Nisan, N. and Veličković, B. (1998), Efficient approximation of product distributions . Random Structures and Algorithms, 13: 1–16. [ pdf ]
- Noga Alon, Dana Moshkovitz, and Shmuel Safra. 2006. Algorithmic construction of sets for k-restrictions. ACM Trans. Algorithms 2, 2 (April 2006), 153-177.

- [ pdf ]
Concatenating the RS-code with the identity code.
A greedy construction. The Porat-Rothschild construction.
- E. Porat, A. Rothschild, "Explicit Non-Adaptive Combinatorial Group Testing Schemes", ICALP'08.
- Sergey Yekhanin, Some new Constructions of Optimal Superimposed Designs [ pdf ]
- Arkadii G. D'yachkov, Anthony J. Macula, Vyacheslav V. Rykov: New constructions of superimposed codes. IEEE Transactions on Information Theory 46(1): 284-290 (2000)
- David Eppstein, Michael T. Goodrich, Daniel S. Hirschberg: Improved Combinatorial Group Testing Algorithms for Real-World Problem Sizes. SIAM J. Comput. 36(5): 1360-1375 (2007)

- Basic complexity results and approximation algorithms.
- [ pdf ] Du, Ding Zhu; Ko, Ker-I Some completeness results on decision trees and group testing. SIAM J. Algebraic Discrete Methods 8 (1987), no. 4, 762–777.
- [ pdf ] Feng(PRC-ZHJ); Du, Ding Zhu(PRC-ASBJ-AM) The complexity of determinacy problem on group testing. Discrete Appl. Math. 28 (1990), no. 1, 71–81.

- [ pdf ] Efficient decoding and list group testing
- [ pdf ] Basic bounds for the number of tests of list disjunct and list separable matrices
- [ pdf ]
A recursive construction of sub-linear time decodable list disjunct matrices
- Hung Q. Ngo, Ely Porat, Atri Rudra: Efficiently Decodable Error-Correcting List Disjunct Matrices and Applications - (Extended Abstract). ICALP (1) 2011: 557-568

- [ pdf ] Constructions of list disjunct matrices based on list-recoverable codes.
- Piotr Indyk, Hung Q. Ngo, Atri Rudra: Efficiently Decodable Non-adaptive Group Testing. SODA 2010: 1126-1142

- [ pdf ] Explicit construction of list disjunct matrices based on randomness extractors and based on expanders.
- Mahdi Cheraghchi: Noise-Resilient Group Testing: Limitations and Constructions. FCT 2009: 62-73

- [ pdf ] Error-correcting (list-) separable and (list-) disjunct matrices. Lower bounds and probabilistic upper bounds.
- Explicit and strongly explicit constructions of error-correcting disjunct matrices
- Explicit and strongly explicit constructions of efficiently decodable
**and**error-correcting list-disjunct matrices - The relative error rate case.

- Variations of the basic group testing paradigm.
- Mahdi Cheraghchi: Improved Constructions for Non-adaptive Threshold Group Testing. ICALP (1) 2010: 552-564

- Group testing on graphs
- Mahdi Cheraghchi, Amin Karbasi, Soheil Mohajer, Venkatesh Saligrama: Graph-Constrained Group Testing CoRR abs/1001.1445: (2010)
- Nicholas J. A. Harvey, Mihai Patrascu, Yonggang Wen, Sergey Yekhanin, Vincent W. S. Chan: Non-Adaptive Fault Diagnosis for All-Optical Networks via Combinatorial Group Testing on Graphs. INFOCOM 2007: 697-705
- M. Wang, W. Xu, E. Mallada and A. Tang. Sparse Recovery with Graph Constraints: Fundamental Limits and Measurement Construction. to appear in IEEE Infocom 2012.
- W. Xu, E. Mallada and A. Tang. Compressive Sensing over Graphs. Proceedings of IEEE Infocom 2011.

- Three applications of list-disjunct matrices.
- Noga Alon, Rani Hod: Optimal Monotone Encodings. IEEE Transactions on Information Theory 55(3): 1343-1353 (2009)
- N. Alon and V. Asodi, Tracing many users with almost no rate penalty, IEEE Transactions on Information Theory 53 (2007), 437-439.
- Ravi Kumar, Sridhar Rajagopalan, Amit Sahai: Coding Constructions for Blacklisting Problems without Computational Assumptions. CRYPTO 1999: 609-623

- Connection to compressive sensing.
- Hung Q. Ngo, Ely Porat, and Atri Rudra, "Efficiently Decodable Compressed Sensing by List-Recoverable Codes and Recursion," in Proceedings of the 29th Symposium on Theoretical Aspects of Computer Science (STACS 2012), Feb 29 –- March 3rd, 2012, Paris, France.

- Applications in pattern matching.
- Applications in cryptography.
- Applications in streaming.