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The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
Open problems around exact algorithms by Gerhard J. Woeginger, Discrete Applied Mathematics 156 (2008) 397–405. The RTA list of open problems – open problems in rewriting. The TLCA List of Open Problems – open problems in area typed lambda calculus
For each combinatorial optimization problem, there is a corresponding decision problem that asks whether there is a feasible solution for some particular measure m 0. For example, if there is a graph G which contains vertices u and v , an optimization problem might be "find a path from u to v that uses the fewest edges".
Determining the optimal solution to VRP is NP-hard, [2] so the size of problems that can be optimally solved using mathematical programming or combinatorial optimization can be limited. Therefore, commercial solvers tend to use heuristics due to the size and frequency of real world VRPs they need to solve.
In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon. It is a special case of point location problems and finds applications in areas that deal with processing geometrical data, such as computer graphics , computer vision , geographic ...
In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them. It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive ...
One of the favorite liberal solutions to Social Security’s financial problems is to eliminate the wage cap entirely but give people who earn more than the cap no benefits above the current formula.
The main purpose of a problem statement is to identify and explain the problem. [3] [4] Another function of the problem statement is as a communication device. [3] Before the project begins, stakeholders verify the problem and goals are accurately described in the problem statement. Once approved, the project reviews it.