Table of Contents
What is combinatorial optimization used for?
Combinatorial optimization is an emerging field at the forefront of combinatorics and theoretical computer science that aims to use combinatorial techniques to solve discrete optimization problems. A discrete optimization problem seeks to determine the best possible solution from a finite set of possibilities.
What is the combinatorial optimization problem?
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set.
Is combinatorial optimization NP hard?
Most of the well-known problems of combinatorial optimisation belong to the class of the so-called NP-hard problems and they are intrinsically very difficult in computation.
Is combinatorial optimization convex?
We introduce the convex combinatorial optimization problem, a far-reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.
Is one of the fundamental combinatorial optimization problems?
The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics. In an assignment problem, we must find a maximum matching that has the minimum weight in a weighted bipartite graph.
What is a combinatorial problem?
A combinatorial problem consists in, given a finite collection of objects and a set of constraints, finding an object of the collection that satisfies all constraints (and possibly that optimizes some objective function). Combinatorial problems are ubiquitous and have an enourmous practical importance.
What is the most difficult in solving combinatorial problems?
But what makes an optimization problem difficult? For combinatorial problems, it is the problem size. Such problems have an exact solution method—just write down all possible solutions and pick the best one—but this approach is almost never feasible for realistic problem sizes.