کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1149939 957904 2008 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Classification of orthogonal arrays by integer programming
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Classification of orthogonal arrays by integer programming
چکیده انگلیسی

The problem of classifying all isomorphism classes of OA(N,k,s,t)OA(N,k,s,t)'s is shown to be equivalent to finding all isomorphism classes of non-negative integer solutions to a system of linear equations under the symmetry group of the system of equations. A branch-and-cut algorithm developed by Margot [2002. Pruning by isomorphism in branch-and-cut. Math. Programming Ser. A 94, 71–90; 2003a. Exploiting orbits in symmetric ILP. Math. Programming Ser. B 98, 3–21; 2003b. Small covering designs by branch-and-cut. Math. Programming Ser. B 94, 207–220; 2007. Symmetric ILP: coloring and small integers. Discrete Optim., 4, 40–62] for solving integer programming problems with large symmetry groups is used to find all non-isomorphic OA(24,7,2,2)OA(24,7,2,2)'s, OA(24,k,2,3)OA(24,k,2,3)'s for 6⩽k⩽116⩽k⩽11, OA(32,k,2,3)OA(32,k,2,3)'s for 6⩽k⩽116⩽k⩽11, OA(40,k,2,3)OA(40,k,2,3)'s for 6⩽k⩽106⩽k⩽10, OA(48,k,2,3)OA(48,k,2,3)'s for 6⩽k⩽86⩽k⩽8, OA(56,k,2,3)OA(56,k,2,3)'s, OA(80,k,2,4)OA(80,k,2,4)'s, OA(112,k,2,4)OA(112,k,2,4)'s, for k=6,7k=6,7, OA(64,k,2,4)OA(64,k,2,4)'s, OA(96,k,2,4)OA(96,k,2,4)'s for k=7,8k=7,8, and OA(144,k,2,4)OA(144,k,2,4)'s for k=8,9k=8,9. Further applications to classifying covering arrays with the minimum number of runs and packing arrays with the maximum number of runs are presented.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 138, Issue 3, 1 March 2008, Pages 654–666
نویسندگان
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