LLL-reduction for integer knapsacks
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Babai L (1986) On Lovász’ lattice reduction and the nearest lattice point problem. Combinatorica 6(1):1–13
Beihoffer D, Hendry J, Nijenhuis A, Wagon S (2005) Faster algorithms for Frobenius numbers. Electron J Comb 12. Research Paper 27, 38 pp (electronic)
Cassels JWS (1971) An introduction to the geometry of numbers. Springer, Berlin
Eisenbrand F, Shmonin G (2008) Parametric integer programming in fixed dimension. Math Oper Res 33(4):839–850
Fukshansky L, Robins S (2007) Frobenius problem and the covering radius of a lattice. Discrete Comput Geom 37(3):471–483
Grötschel M, Lovász L, Schrijver A (1988) Geometric algorithms and combinatorial optimization. Algorithms and combinatorics: study and research texts, vol 2. Springer, Berlin
Gruber PM (2007) Convex and discrete geometry. Springer, Berlin
Gruber PM, Lekkerkerker CG (1987) Geometry of numbers. North-Holland, Amsterdam
Kannan R (1992) Lattice translates of a polytope and the Frobenius problem. Combinatorica 12(2):161–177
Lee J, Onn S, Weismantel R (2009) Approximate nonlinear optimization over a weighted independence systems. SIAM J Discrete Math 23:1667–1681
Lenstra AK, Lenstra HW Jr., Lovász L (1982) Factoring polynomials with rational coefficients. Math Ann 261(4):515–534
Martinet J (2003) Perfect lattices in Euclidean spaces. Grundlehren der Mathematischen Wissenschaften, vol 327. Springer, Berlin
McMullen P (1984) Determinants of lattices induced by rational subspaces. Bull Lond Math Soc 16(3):275–277
Papadimitriou CH, Steiglitz K (1998) Combinatorial optimization: algorithms and complexity. Dover, Mineola
Pleasants P, Ray H, Simpson J (2005) The Frobenius problem on lattices. Australas J Comb 32:27–45
Ramírez Alfonsín JL (2005) The Diophantine Frobenius problem. Oxford lecture series in mathematics and its applications
Schrijver A (1986) Theory of linear and integer programming. Wiley, Chichester
Simpson RJ, Tijdeman R (2003) Multi-dimensional versions of a theorem of Fine and Wilf and a formula of Sylvester. Proc Am Math Soc 131(6):1661–1671