Approximation algorithmIn computer science and operations research, approximation algorithms are efficientalgorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture.
Travelling salesman problemNP-hard problem in combinatorial optimizationThe travelling salesman problem seeks to find the shortest possible loop that connects every red dot.Solution of the above problemIn the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?"
Knapsack problemProblem in combinatorial optimizationExample of a one-dimensional (constraint) knapsack problem: which books should be chosen to maximize the books' value while still keeping the overall weight under or equal to 15 kg? A multiple constrained problem could consider both the weight and volume of the books.
Computational complexity theoryIn theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer and is solvable by mechanical application of mathematical steps, such as an algorithm.
Operations researchOperations research (British English: operational research), often shortened to the initialismOR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and decision-making. The term management science is occasionally used as a synonym.
AlgorithmIn mathematics and computer science, an algorithm () is any well-defined set of instructions that when followed terminates after a finite number of steps that comprise a solution to a given computational problem. Advanced algorithms may utilize loops and involve many conditionals that decide the next step based on the inputs provided, resulting in long sequences of steps before halting, but all algorithms terminate by definition.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization.
Feasible regionIn mathematical optimization and computer science, a feasible region,feasible set, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.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 numbern would enumerate all integers from 1 to n, and check whether each of them divides n without remainder.
Machine learningSubset of artificial intelligenceMachine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data, and thus perform tasks without being explicitly programmed. Statistics and mathematical optimisation methods compose the foundations of machine learning.
Minimum spanning treeIn graph theory, a minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. That is, it is a spanning tree whose sum of edge weights is as small as possible.
Artificial intelligenceIntelligence in machinesArtificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making.
Finite setIn mathematics, a finite set is a collection of finitely many different things; the things are called elements or members of the set and are typically mathematical objects, such as numbers, symbols, points in space, lines, other geometric shapes, variables, or other sets. Informally, a finite set is a set which one could in principle count and finish counting. For example, { 2 , 4 , 6 , 8 , 10 } {\displaystyle \{2,4,6,8,10\}} is a finite set with five elements.*As an Amazon Associate I earn from qualifying purchases.