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@article{SEMR_2023_20_1_a2, author = {A. N. Rybalov}, title = {Generic polynomial algorithms for the knapsack problem in some matrix semigroups}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {100--109}, publisher = {mathdoc}, volume = {20}, number = {1}, year = {2023}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a2/} }
TY - JOUR AU - A. N. Rybalov TI - Generic polynomial algorithms for the knapsack problem in some matrix semigroups JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2023 SP - 100 EP - 109 VL - 20 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a2/ LA - ru ID - SEMR_2023_20_1_a2 ER -
A. N. Rybalov. Generic polynomial algorithms for the knapsack problem in some matrix semigroups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 100-109. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a2/
[1] S. Birmpilis, G. Labahn, A. Storjohann, “A fast algorithm for computing the Smith normal form with multipliers for a nonsingular integer matrix”, J. Symb. Comput., 116 (2023), 146–182 | DOI | MR | Zbl
[2] V. Cacchiani, M. Iori, A. Locatelli, S. Martello, “Knapsack problems – an overview of recent advances. I: Single knapsack problems”, Comput. Oper. Res., 143 (2022), 105692 | DOI | MR | Zbl
[3] V. Cacchiani, M. Iori, A. Locatelli, S. Martello, “Knapsack problems - an overview of recent advances. II: Multiple, multidimensional, and quadratic knapsack problems”, Comput. Oper. Res., 143 (2022), 105693 | DOI | MR | Zbl
[4] M. Garey, D. Johnson, Computers and intractability. A guide to the theory of NP-completeness, W.H. Freeman and Company, San Francisco, 1979 | MR | Zbl
[5] D. Hirschfeldt, “Some questions in computable mathematics”, Computability and complexity. Essays dedicated to Rodney G. Downey on the occasion of his 60th birthday, eds. Day Adam et al., Springer, Cham, 2017, 22–55 | DOI | MR | Zbl
[6] C. Jockusch, P. Schupp, “Generic computability, Turing degrees, and asymptotic density”, J. Lond. Math. Soc., II. Ser., 85:2 (2012), 472–490 | DOI | MR | Zbl
[7] I. Kapovich, A. Myasnikov, P. Schupp, V. Shpilrain, “Generic-case complexity, decision problems in group theory, and random walks”, J. Algebra, 264:2 (2003), 665–694 | DOI | MR | Zbl
[8] R. Karp, “Reducibility among combinatorial problems”, Complexity of Computer Computations, Plenum Press, New York, 1973, 85–103 | MR | Zbl
[9] E. Karstadt, O. Schwartz, “Matrix multiplication, a little faster”, J. ACM, 67:1 (2020), 1 | DOI | MR | Zbl
[10] A. Miasnikov, A. Nikolaev, A. Ushakov, “Knapsack problems in groups”, Math. Comput., 84:292 (2015), 987–1016 | DOI | MR | Zbl
[11] V. Neiger, C. Pernet, “Deterministic computation of the characteristic polynomial in the time of matrix multiplication”, J. Complexity, 67 (2021), 101572 | DOI | MR | Zbl
[12] J. Nielsen, “Die Gruppe der dreidimensionalen Gittertransformationen”, Kgl. Danske Vid. Selsk., Math.-fys. Medd., 5:12 (1924), 3–29 | Zbl
[13] A. Rosowski, “Fast commutative matrix algorithms”, J. Symb. Comput., 114 (2023), 302–321 | DOI | MR | Zbl
[14] A. Rybalov, “On generic complexity of the subset sum problem for semigroups of integer matrices”, Prikl. Diskretn. Mat., 50 (2020), 118–126 | MR | Zbl
[15] A. Rybalov, “O genericheskoi slozhnosti problemy o summe podmnozhestv v monoidakh i gruppakh tselochislennykh matrits vtorogo poryadka”, Vestnik Omskogo universiteta, 25:4 (2020), 10–15
[16] S.M. Shperling, Y.A. Kochetov, “A knapsack problem for rectangles under center-of-gravity constraints”, J. Appl. Ind. Math., 16:3 (2022), 563–571 | DOI | MR
[17] V. Strassen, “Gaussian elimination is not optimal”, Numer. Math., 13:4 (1969), 354–356 | DOI | MR | Zbl
[18] S. Winograd, “On multiplication of $2 \times 2$ matrices”, Linear Algebra Appl., 4 (1971), 381–388 | DOI | MR | Zbl