Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based...

integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers...

variables are required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. In contrast to linear...

software updates to legacy systems address this problem by using signed 64-bit integers instead of 32-bit integers, which will take 292 billion years to overflow—approximately...

Learning with errors Short integer solution problem Khot, Subhash (2005). "Hardness of approximating the shortest vector problem in lattices". J. ACM...

Corporation, who expressed the problem as an integer linear program and developed the cutting plane method for its solution. They wrote what is considered...

sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and...

the integers that have the same total. This problem is contained in PPP, but it is not known if it is PPP-complete. The constrained-SIS (short integer solution)...

problem in computer science If the solution to a problem is easy to check for correctness, must the problem be easy to solve? More unsolved problems in...

Knapsack Problem Archived 14 February 2015 at the Wayback Machine Optimizing Three-Dimensional Bin Packing Knapsack Integer Programming Solution in Python...

Znám's problem asks which sets of integers have the property that each integer in the set is a proper divisor of the product of the other integers in the...

computational problem is one that asks for a solution in terms of an algorithm. For example, the problem of factoring "Given a positive integer n, find a...

principal contributors to its solution). When all coefficients and variables are restricted to be positive integers, the related problem of polynomial identity...

logarithm problem. Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents...

problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem. A paper machine can produce an unlimited...

economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two...

1741. The solution to this problem can be used to estimate the probability that two large random numbers are coprime. Two random integers in the range...

In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and...

of items is clear from the context. A possible integer linear programming formulation of the problem is: where y j = 1 {\displaystyle y_{j}=1} if bin...

state SIS (file format), Symbian OS filename extension Short integer solution problem, a problem in lattice-based cryptography Single-instance storage...

weakly-polynomial. If the weights are integers, and all weights are at most C (where C>1 is some integer), then the problem can be solved in O ( m n log ⁡ (...

Hilbert's tenth problem: the problem of deciding whether a Diophantine equation (multivariable polynomial equation) has a solution in integers. For functions...

x will need to take on integer values. This leads to the formulation of a mixed-integer quadratic programming (MIQP) problem. Applications of MIQP include...

including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has...

polynomial equation in two or more unknowns with integer coefficients, for which only integer solutions are of interest. A linear Diophantine equation equates...

The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a...

self-reducible, because deciding whether an integer is prime is in P (easy), while the integer factorization problem is believed to be hard for a classical...

these kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP)...

Unsolved problem in mathematics Does n ! + 1 = m 2 {\displaystyle n!+1=m^{2}} have integer solutions other than n = 4 , 5 , 7 {\displaystyle n=4,5,7}...

In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of...