Some lattice point problems

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Rational Generating Functions for Lattice Point Problems

We prove that for any fixed d the generating function of the projection of the set of integer points in a rational d-dimensional polytope can be computed in polynomial time. As a corollary, we deduce that various interesting sets of lattice points, notably integer semigroups and (minimal) Hilbert bases of rational cones, have short rational generating functions provided certain parameters (the ...

متن کامل

Improved Convexity Cuts for Lattice Point Problems

The generalized lattice point (GLF) problem provides a formulation that accommodates a var.lety of discrete alternative problems. In this paper we show how to substantlrlly strengthen the convexity cuts for the GLF problem. The new cuts are based on the identification of "synthesized" lattice point conditions to replace those that ordinarily define the cut. The synthesized conditions give an al...

متن کامل

Some Exact Results for Quantum Lattice Problems

Physics is increasingly moving towards nano-scale technology, and with this comes the need to understand small lattices or quasi-lattices supporting a small number of quanta. Often this gives the quantum equivalent of a classical breather, though with some interesting differences. In this short paper we review some work on quantum lattice problems, concentrating mainly on the quantum discrete n...

متن کامل

Some Sieving Algorithms for Lattice Problems

We study the algorithmic complexity of lattice problems based on the sieving technique due to Ajtai, Kumar, and Sivakumar [AKS01]. Given a k-dimensional subspace M ⊆ Rn and a full rank integer lattice L ⊆ Qn, the subspace avoiding problem SAP, defined by Blömer and Naewe [BN07], is to find a shortest vector in L \ M. We first give a 2O(n+k log k) time algorithm to solve the subspace avoiding pr...

متن کامل

Some Preconditioning Techniques for Saddle Point Problems

Saddle point problems arise frequently in many applications in science and engineering, including constrained optimization, mixed finite element formulations of partial differential equations, circuit analysis, and so forth. Indeed the formulation of most problems with constraints gives rise to saddle point systems. This paper provides a concise overview of iterative approaches for the solution...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Bulletin of the Australian Mathematical Society

سال: 1980

ISSN: 0004-9727,1755-1633

DOI: 10.1017/s0004972700006109