A mathematical programming approach to the construction of BIBDs

References

• Anderson , I. 2006 . Combinatorial Designs and Tournaments , New York : Oxford University Press .
   Google Scholar
• Beth , T. , Jungnickel , D. and Lenz , H. 1999 . Design Theory , 2 , Cambridge : Cambridge University Press .
   Google Scholar
• Biggs , N. L. , Lloyd , E. K. and Wilson , R. J. 1995 . The history of combinatorics, in Handbook of Combinatorics , Edited by: Graham , R. L. , Grötschel , M. and Lovász , L. Vol. II , 2163 – 2198 . Amsterdam : Elsevier .
   Google Scholar
• Bilous , R. , Lam , C. W.H. , Thiel , L. H. , Li , B. P.C. , van Rees , G. H.J. , Radziszowski , S. P. , Holzmann , W. H. and Kharaghani , H. 2006 . There is no 2-(22, 8, 4) block design . J. Combin. Des. , 15 : 262 – 267 .
   Google Scholar
• Bofill , P. , Guimera , R. and Torras , C. 2003 . Comparison of simulated annealing and mean field annealing as applied to the generation of block designs . Neural Netw. , 16 : 1421 – 1428 .
   PubMed Web of Science ®Google Scholar
• Box , G. E. , Hunter , W. G. and Hunter , J. S. 2005 . Statistics for Experimenters: Design, Innovation, and Discovering , 2 , Hoboken : John Wily & Sons .
   Google Scholar
• Brouwer , E. 1995 . Block designs, in Handbook of Combinatorics , Edited by: Graham , R. , Gröetschel , M. and Lovász , L. Vol. I , 693 – 771 . Amsterdam : Elsevier .
   Google Scholar
• Colbourn , C. J. and Dinitz , J. H. 2007 . Handbook of Combinatorial Designs , 2 , New York : Chapman & Hall/CRC .
   Google Scholar
• CPLEX Ver. 11.0, ILOG, 2008. Available at http://www.ilog.com/products/cplex/
   Google Scholar
• Du , D.-Z. and Hwang , F. K. 2000 . Combinatorial Group Testing and its Applications , 2 , Singapore : World Scientific Publication .
   Google Scholar
• Glover , F. and Laguna , M. 1997 . “ Tabu Search ” . Norwell : Kluwer .
   Google Scholar
• Hall , M. Jr. 1998 . Combinatorial Theory , 2 , New York : John Wiley & Sons .
   Google Scholar
• Hanani , H. 1961 . The existence and construction of balanced incomplete block designs . Ann. Math. Stat. , 32 : 361 – 386 .
   Google Scholar
• Hanani , H. 1975 . Balanced incomplete block designs and related designs . Discrete Math. , 11 : 255 – 369 .
   Web of Science ®Google Scholar
• Houghten , S. K. , Thiel , L. H. , Janssen , J. and Lamet , C. W.H. 2001 . There is no (46,6,1) block design . J. Combin. Des. , 9 : 60 – 71 .
   Google Scholar
• Kirkman , T. 1847 . On a problem in combinations . Cambridge Dublin Math. J. , 2 : 191 – 204 .
   Google Scholar
• Kreher , D. L. and Stinson , D. R. 1999 . Combinatorial Algorithms: Generation, Enumeration and Search , Boca Raton : CRC Press .
   Google Scholar
• Kurokawa , T. and Takefuji , Y. 1992 . Neural network parallel computing for BIBD problems . IEEE Trans. Circuits Syst. II , 39 : 243 – 247 .
   Google Scholar
• Morales , L. B. 2000 . Constructing difference families through an optimization approach: Six new BIBDs . J. Combin. Des. , 8 : 261 – 273 .
   Google Scholar
• Prestwich , S. Balanced incomplete block design as satisfiability . Irish Conference on AI and Cognitive Science . Cork. Vol. 12 , pp. 189 – 198 .
   Google Scholar
• Prestwich , S. 2002 . A local search algorithm for balanced incomplete block designs , Cork : University College Cork . Lecture Notes in Artificial Intelligence, Cork Constraint Computation Centre
   Google Scholar
• Sachkov , V. N. 1977 . Combinatorial Methods in Discrete Mathematics , Cambridge : Cambridge University Press .
   Google Scholar
• Schrijver , A. 1998 . Theory of Linear and Integer Programming , Amsterdam : John Wiley & Sons .
   Google Scholar
• Sedegewick , R. 1998 . Algorithms in C , 3 , Boston : Addison-Wesley .
   Google Scholar
• Stinson , D. R. 2004 . Combinatorial Designs: Construction and Analysis , New York : Springer-Verlag .
   Google Scholar