Time complexityIn computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor.
Set cover problemThe set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 1972. Given a set of elements {1, 2, ..., n} (called the universe) and a collection S of m sets whose union equals the universe, the set cover problem is to identify the smallest sub-collection of S whose union equals the universe. For example, consider the universe U = {1, 2, 3, 4, 5} and the collection of sets S = { {1, 2, 3}, {2, 4}, {3, 4}, {4, 5} }.
A-levelThe A-level (Advanced Level) is a subject-based qualification conferred as part of the General Certificate of Education, as well as a school leaving qualification offered by the educational bodies in the United Kingdom and the educational authorities of British Crown dependencies to students completing secondary or pre-university education. They were introduced in England and Wales in 1951 to replace the Higher School Certificate. The A-level permits students to have potential access to university if their grade is of satisfactory quality.
Brute-force searchIn computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique and algorithmic paradigm that consists of systematically checking all possible candidates for whether or not each candidate satisfies the problem's statement. A brute-force algorithm that finds the divisors of a natural number n would enumerate all integers from 1 to n, and check whether each of them divides n without remainder.
Optimization problemIn mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
Relaxation (iterative method)In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems. Relaxation methods were developed for solving large sparse linear systems, which arose as finite-difference discretizations of differential equations. They are also used for the solution of linear equations for linear least-squares problems and also for systems of linear inequalities, such as those arising in linear programming. They have also been developed for solving nonlinear systems of equations.
Assignment problemThe assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform as many tasks as possible by assigning at most one agent to each task and at most one task to each agent, in such a way that the total cost of the assignment is minimized.
Linear complementarity problemIn mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968. Given a real matrix M and vector q, the linear complementarity problem LCP(q, M) seeks vectors z and w which satisfy the following constraints: (that is, each component of these two vectors is non-negative) or equivalently This is the complementarity condition, since it implies that, for all , at most one of and can be positive.
Job-shop schedulingJob-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan – the total length of the schedule (that is, when all the jobs have finished processing).
SolverA solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculates their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type. Types of problems with existing dedicated solvers include: Linear and non-linear equations.
