메뉴 건너뛰기




Volumn 34, Issue 5, 2005, Pages 1253-1270

Optimal two-stage algorithms for group testing problems

Author keywords

Cover free families; Group testing

Indexed keywords

BIOLOGICAL SCREENING; COVER-FREE FAMILIES; GROUP TESTING; TWO-STAGE ALGORITHMS;

EID: 27144547067     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539703428002     Document Type: Article
Times cited : (134)

References (56)
  • 2
    • 0003668374 scopus 로고
    • Wiley-Teubner, New York, Stuttgart
    • M. AIGNER, Combinatorial Search, Wiley-Teubner, New York, Stuttgart, 1988.
    • (1988) Combinatorial Search
    • Aigner, M.1
  • 3
    • 27144531541 scopus 로고    scopus 로고
    • Learning a hidden subgraph
    • N. ALON AND V. ASODI, Learning a hidden subgraph, SIAM J. Discrete Math., 18 (2005), pp. 697-712.
    • (2005) SIAM J. Discrete Math. , vol.18 , pp. 697-712
    • Alon, N.1    Asodi, V.2
  • 4
    • 0000710299 scopus 로고
    • Queries and concept learning
    • D. ANGLUIN, Queries and concept learning, Mach. Learn., 2 (1987), pp. 319-342.
    • (1987) Mach. Learn. , vol.2 , pp. 319-342
    • Angluin, D.1
  • 5
    • 0026072844 scopus 로고
    • Theoretical analysis of library screening using an n-dimensional pooling strategy
    • E. BARILLOT, B. LACROIX, AND D. COHEN, Theoretical analysis of library screening using an n-dimensional pooling strategy, Nucleic Acids Res., 19 (1991), pp. 6241-6247.
    • (1991) Nucleic Acids Res. , vol.19 , pp. 6241-6247
    • Barillot, E.1    Lacroix, B.2    Cohen, D.3
  • 6
    • 0004465320 scopus 로고    scopus 로고
    • A comparative survey of non-adaptive pooling design
    • Genetic Mapping and DNA Sequencing, T. P. Speed and M. S. Waterman, eds., Springer-Verlag, Berlin
    • D. J. BALDING, W. J. BRUNO, E. KNILL, AND D. C. TORNEY, A comparative survey of non-adaptive pooling design, in Genetic Mapping and DNA Sequencing, IMA Vol. Math. Appl. 81, T. P. Speed and M. S. Waterman, eds., Springer-Verlag, Berlin, 1996, pp. 133-154.
    • (1996) IMA Vol. Math. Appl. , vol.81 , pp. 133-154
    • Balding, D.J.1    Bruno, W.J.2    Knill, E.3    Torney, D.C.4
  • 7
    • 0036649488 scopus 로고    scopus 로고
    • Asymptotic efficiency of two-stage disjunctive testing
    • T. BERGER AND V. I. LEVENSHTEIN, Asymptotic efficiency of two-stage disjunctive testing, IEEE Trans. Inform. Theory, 48 (2002), pp. 1741-1749.
    • (2002) IEEE Trans. Inform. Theory , vol.48 , pp. 1741-1749
    • Berger, T.1    Levenshtein, V.I.2
  • 8
    • 0038060503 scopus 로고    scopus 로고
    • Application of cover-free codes and combinatorial design to two-stage testing
    • T. BERGER AND V. I. LEVENSHTEIN, Application of cover-free codes and combinatorial design to two-stage testing, Discrete Appl. Math., 128 (2003), pp. 11-26.
    • (2003) Discrete Appl. Math. , vol.128 , pp. 11-26
    • Berger, T.1    Levenshtein, V.I.2
  • 9
    • 0033851705 scopus 로고    scopus 로고
    • Maximally efficient two-stage screening
    • T. BERGER, J. W. MANDELL, AND P. SUBRAHMANYA, Maximally efficient two-stage screening, Biometrics, 56 (2000), pp. 833-840.
    • (2000) Biometrics , vol.56 , pp. 833-840
    • Berger, T.1    Mandell, J.W.2    Subrahmanya, P.3
  • 11
    • 27144442020 scopus 로고
    • Constructive methods to solve problems of s-surjectivity, conflict resolution, and coding in defective memories
    • Ecole Nationale des Telecomm., ENST Paris
    • P. BUSSBACH, Constructive Methods to Solve Problems of s-surjectivity, Conflict Resolution, and Coding in Defective Memories, Tech. report 84D005, Ecole Nationale des Telecomm., ENST Paris, 1984.
    • (1984) Tech. Report , vol.84 D005
    • Bussbach, P.1
  • 13
    • 0036591068 scopus 로고    scopus 로고
    • Fast broadcasting and gossiping in radio networks
    • M. CHROBAK, L. GA̧SIENIEC, AND W. RYTTER, Fast broadcasting and gossiping in radio networks, J. Algorithms, 43 (2002), pp. 177-189.
    • (2002) J. Algorithms , vol.43 , pp. 177-189
    • Chrobak, M.1    Ga̧sieniec, L.2    Rytter, W.3
  • 14
    • 0037028452 scopus 로고    scopus 로고
    • Least adaptive optimal search with unreliable tests
    • F. CICALESE, D. MUNDICI, AND U. VACCARO, Least adaptive optimal search with unreliable tests, Theoret. Comput. Sci., 270 (2002), pp. 877-893.
    • (2002) Theoret. Comput. Sci. , vol.270 , pp. 877-893
    • Cicalese, F.1    Mundici, D.2    Vaccaro, U.3
  • 18
    • 0346478925 scopus 로고    scopus 로고
    • Parallel attribute-efficient learning of monotone Boolean functions
    • Algorithm Theory - SWAT 2000, M. M. Halldórsson, ed., Springer-Verlag, Berlin
    • P. DAMASCHKE, Parallel attribute-efficient learning of monotone Boolean functions, in Algorithm Theory - SWAT 2000, Lecture Notes in Comput. Sci. 1851, M. M. Halldórsson, ed., Springer-Verlag, Berlin, 2000, pp. 504-512.
    • (2000) Lecture Notes in Comput. Sci. , vol.1851 , pp. 504-512
    • Damaschke, P.1
  • 19
    • 84961304819 scopus 로고    scopus 로고
    • Computational aspects of parallel attribute-efficient learning
    • Proceedings of the 9th International Conference on Algorithmic Learning Theory, M. Richter et al., eds., Springer-Verlag, Berlin
    • P. DAMASCHKE, Computational aspects of parallel attribute-efficient learning, in Proceedings of the 9th International Conference on Algorithmic Learning Theory, Lecture Notes in Comput. Sci. 1501, M. Richter et al., eds., Springer-Verlag, Berlin, 1998, pp. 103-111.
    • (1998) Lecture Notes in Comput. Sci. , vol.1501 , pp. 103-111
    • Damaschke, P.1
  • 20
    • 0042941302 scopus 로고    scopus 로고
    • Randomized group testing for mutually obscuring defectives
    • P. DAMASCHKE, Randomized group testing for mutually obscuring defectives, Inform. Process. Lett., 67 (1998), pp. 131-135.
    • (1998) Inform. Process. Lett. , vol.67 , pp. 131-135
    • Damaschke, P.1
  • 21
    • 0032120173 scopus 로고    scopus 로고
    • Improved algorithms for group testing with inhibitors
    • A. DE BONIS AND U. VACCARO, Improved algorithms for group testing with inhibitors, Inform. Process. Lett., 66 (1998), pp. 57-64.
    • (1998) Inform. Process. Lett. , vol.66 , pp. 57-64
    • De Bonis, A.1    Vaccaro, U.2
  • 22
    • 0042008122 scopus 로고    scopus 로고
    • Constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels
    • A. DE BONIS AND U. VACCARO, Constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels, Theoret. Comput. Sci., 306 (2003), pp. 223-243.
    • (2003) Theoret. Comput. Sci. , vol.306 , pp. 223-243
    • De Bonis, A.1    Vaccaro, U.2
  • 23
    • 0001243071 scopus 로고
    • The detection of defective members of large populations
    • R. DORFMAN, The detection of defective members of large populations, Ann. Math. Statist., 14 (1943), pp. 436-440.
    • (1943) Ann. Math. Statist. , vol.14 , pp. 436-440
    • Dorfman, R.1
  • 26
    • 0036046072 scopus 로고    scopus 로고
    • Families of finite sets in which no intersection of ℓ sets is covered by the union of s others
    • A. G. DYACHKOV, P. VILENKIN, A. MACULA, AND D. TORNEY, Families of finite sets in which no intersection of ℓ sets is covered by the union of s others, J. Combin. Theory Ser. A, 99 (2002), pp. 195-218.
    • (2002) J. Combin. Theory Ser. A , vol.99 , pp. 195-218
    • Dyachkov, A.G.1    Vilenkin, P.2    Macula, A.3    Torney, D.4
  • 27
    • 27144538205 scopus 로고    scopus 로고
    • Private communication
    • A. G. DYACHKOV, Private communication, 2003.
    • (2003)
    • Dyachkov, A.G.1
  • 28
    • 51249175955 scopus 로고
    • Families of finite sets in which no set is covered by the union of r others
    • P. ERDÖS, P. FRANKL, AND Z. FÜREDI, Families of finite sets in which no set is covered by the union of r others, Israel J. Math., 51 (1985), pp. 75-89.
    • (1985) Israel J. Math. , vol.51 , pp. 75-89
    • Erdös, P.1    Frankl, P.2    Füredi, Z.3
  • 29
    • 0031376063 scopus 로고    scopus 로고
    • Group testing problems with sequences in experimental molecular biology
    • B. Carpentieri, A. De Santis, U. Vaccaro, and J. Storer, eds., IEEE, Piscataway, NJ
    • M. FARACH, S. KANNAN, E. H. KNILL, AND S. MUTHUKRISHNAN, Group testing problems with sequences in experimental molecular biology, in Proceedings of Compression and Complexity of Sequences, B. Carpentieri, A. De Santis, U. Vaccaro, and J. Storer, eds., IEEE, Piscataway, NJ, 1997, pp. 357-367.
    • (1997) Proceedings of Compression and Complexity of Sequences , pp. 357-367
    • Farach, M.1    Kannan, S.2    Knill, E.H.3    Muthukrishnan, S.4
  • 30
    • 0001329796 scopus 로고    scopus 로고
    • On r-cover free families
    • Z. FÜREDI, On r-cover free families, J. Combin. Theory Ser. A, 73 (1996), pp. 172-173.
    • (1996) J. Combin. Theory Ser. A , vol.73 , pp. 172-173
    • Füredi, Z.1
  • 31
    • 0036688327 scopus 로고    scopus 로고
    • Group testing for image compression
    • E. H. HONG AND R. E. LADNER, Group testing for image compression, IEEE Trans. Image Process., 11 (2002), pp. 901-911.
    • (2002) IEEE Trans. Image Process. , vol.11 , pp. 901-911
    • Hong, E.H.1    Ladner, R.E.2
  • 32
    • 0041464246 scopus 로고    scopus 로고
    • A survey on combinatorial group testing algorithms with applications to DMA library screening
    • Discrete Mathematical Problems with Medical Applications, AMS, Providence, RI
    • H. Q. NGO AND D.-Z. DU, A survey on combinatorial group testing algorithms with applications to DMA library screening, in Discrete Mathematical Problems with Medical Applications, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 55, AMS, Providence, RI, 2000, pp. 171-182.
    • (2000) DIMACS Ser. Discrete Math. Theoret. Comput. Sci. , vol.55 , pp. 171-182
    • Ngo, H.Q.1    Du, D.-Z.2
  • 33
    • 0038359109 scopus 로고    scopus 로고
    • Error-tolerant pooling designs with inhibitors
    • F. K. HWANG AND Y. C. LIU, Error-tolerant pooling designs with inhibitors, J. Comput. Biol., 10 (2003), pp. 231-236.
    • (2003) J. Comput. Biol. , vol.10 , pp. 231-236
    • Hwang, F.K.1    Liu, Y.C.2
  • 35
    • 0037962389 scopus 로고    scopus 로고
    • Explicit constructions of selectors and related combinatorial structures, with applications
    • SIAM, Philadelphia, ACM, New York
    • P. INDYK, Explicit constructions of selectors and related combinatorial structures, with applications, in Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'02), SIAM, Philadelphia, ACM, New York, 2002, pp. 697-704.
    • (2002) Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'02) , pp. 697-704
    • Indyk, P.1
  • 38
    • 0022037993 scopus 로고
    • An asymptotically fast non-adaptive algorithm for conflict resolution in multiple-access channels
    • J. KOMLÓS AND A. G. GREENBERG, An asymptotically fast non-adaptive algorithm for conflict resolution in multiple-access channels, IEEE Trans. Inform. Theory, 31 (1985), pp. 302-306.
    • (1985) IEEE Trans. Inform. Theory , vol.31 , pp. 302-306
    • Komlós, J.1    Greenberg, A.G.2
  • 39
    • 84957057937 scopus 로고    scopus 로고
    • Coding constructions for blacklisting problems without computational assumptions
    • Proceedings of the 19th Annual International Cryptology Conference (CRYPTO '99), Springer-Verlag, Berlin
    • R. KUMAR, S. RAJAGOPALAN, AND A. SAHAI, Coding constructions for blacklisting problems without computational assumptions, in Proceedings of the 19th Annual International Cryptology Conference (CRYPTO '99), Lecture Notes in Comput. Sci. 1666, Springer-Verlag, Berlin, 1999, pp. 609-623.
    • (1999) Lecture Notes in Comput. Sci. , vol.1666 , pp. 609-623
    • Kumar, R.1    Rajagopalan, S.2    Sahai, A.3
  • 40
    • 0000574140 scopus 로고
    • A sequential method for screening experimental variables
    • C. H. LI, A sequential method for screening experimental variables, J. Amer. Statist. Assoc., 57 (1962), pp. 455-477.
    • (1962) J. Amer. Statist. Assoc. , vol.57 , pp. 455-477
    • Li, C.H.1
  • 41
    • 0026821081 scopus 로고
    • Locality in distributed graph algorithms
    • N. LINIAL, Locality in distributed graph algorithms, SIAM J. Comput., 21 (1992), pp. 193-201.
    • (1992) SIAM J. Comput. , vol.21 , pp. 193-201
    • Linial, N.1
  • 42
    • 0000203509 scopus 로고
    • On the ratio of optimal integral and fractional covers
    • L. LOVÁSZ, On the ratio of optimal integral and fractional covers, Discrete Math., 13 (1975), pp. 383-390.
    • (1975) Discrete Math. , vol.13 , pp. 383-390
    • Lovász, L.1
  • 43
    • 0043000772 scopus 로고    scopus 로고
    • Probabilistic nonadaptive and two-stage group testing with relatively small pools and DNA library screening
    • A. J. MACULA, Probabilistic nonadaptive and two-stage group testing with relatively small pools and DNA library screening, J. Comb. Optim., 2 (1999), pp. 385-397.
    • (1999) J. Comb. Optim. , vol.2 , pp. 385-397
    • Macula, A.J.1
  • 44
    • 0347109117 scopus 로고    scopus 로고
    • Two-stage group testing for complexes in the presence of errors
    • Discrete Mathematical Problems with Medical Applications, AMS, Providence, RI
    • A. J. MACULA, P. VILENKIN, AND D. TORNEY, Two-stage group testing for complexes in the presence of errors, in Discrete Mathematical Problems with Medical Applications, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 55, AMS, Providence, RI, 2000, pp. 145-157.
    • (2000) DIMACS Ser. Discrete Math. Theoret. Comput. Sci. , vol.55 , pp. 145-157
    • Macula, A.J.1    Vilenkin, P.2    Torney, D.3
  • 47
    • 0024959760 scopus 로고
    • Weakly adaptive comparison searching
    • A. PELC, Weakly adaptive comparison searching, Theoret. Comput. Sci., 66 (1989), pp. 105-111.
    • (1989) Theoret. Comput. Sci. , vol.66 , pp. 105-111
    • Pelc, A.1
  • 48
    • 0037028458 scopus 로고    scopus 로고
    • Searching games with errors - Fifty years of coping with liars
    • A. PELC, Searching games with errors - fifty years of coping with liars, Theoret. Comput. Sci., 243 (2002), pp. 71-109.
    • (2002) Theoret. Comput. Sci. , vol.243 , pp. 71-109
    • Pelc, A.1
  • 49
    • 85010085813 scopus 로고
    • Towards DNA sequencing chips
    • Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science, Springer-Verlag, Berlin
    • P. A. PEVZNER AND R. J. LIPSHUTZ, Towards DNA sequencing chips, in Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Comput. Sci. 841, Springer-Verlag, Berlin, 1994, pp. 143-158.
    • (1994) Lecture Notes in Comput. Sci. , vol.841 , pp. 143-158
    • Pevzner, P.A.1    Lipshutz, R.J.2
  • 51
    • 38149147626 scopus 로고
    • On the upper bound of the size of the r-cover-free families
    • M. RUSZINKÓ, On the upper bound of the size of the r-cover-free families, J. Combin. Theory Ser. A, 66 (1994), pp. 302-310.
    • (1994) J. Combin. Theory Ser. A , vol.66 , pp. 302-310
    • Ruszinkó, M.1
  • 52
    • 84944483668 scopus 로고
    • Group testing to eliminate efficiently all defectives in a binomial sample
    • M. SOBEL AND P. A. GROLL, Group testing to eliminate efficiently all defectives in a binomial sample, Bell System Tech. J., 38 (1959), pp. 1179-1252.
    • (1959) Bell System Tech. J. , vol.38 , pp. 1179-1252
    • Sobel, M.1    Groll, P.A.2
  • 53
    • 0026839843 scopus 로고
    • Ulam's searching game with a fixed number of lies
    • J. SPENCER, Ulam's searching game with a fixed number of lies, Theoret. Comput. Sci., 95 (1992), pp. 307-321.
    • (1992) Theoret. Comput. Sci. , vol.95 , pp. 307-321
    • Spencer, J.1
  • 54
    • 0000137420 scopus 로고    scopus 로고
    • Secure frameproof codes, key distribution patterns, group testing algorithms and related structures
    • D. R. STINSON, T. VAN TRUNG, AND R. WEI, Secure frameproof codes, key distribution patterns, group testing algorithms and related structures, J. Statist. Plann. Inference, 86 (2000), pp. 595-617.
    • (2000) J. Statist. Plann. Inference , vol.86 , pp. 595-617
    • Stinson, D.R.1    Van Trung, T.2    Wei, R.3
  • 55
    • 0022037454 scopus 로고
    • Born again group testing: Multiaccess communications
    • J. WOLF, Born again group testing: Multiaccess communications, IEEE Trans. Inform. Theory, 31 (1985), pp. 185-191.
    • (1985) IEEE Trans. Inform. Theory , vol.31 , pp. 185-191
    • Wolf, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.