Category: NP-hard problems

K-minimum spanning tree
The k-minimum spanning tree problem, studied in theoretical computer science, asks for a tree of minimum cost that has exactly k vertices and forms a subgraph of a larger graph. It is also called the
Vertex k-center problem
The vertex k-center problem is a classical NP-hard problem in computer science. It has application in facility location and clustering. Basically, the vertex k-center problem models the following real
Travelling salesman problem
The travelling salesman problem (also called the travelling salesperson problem or TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the
In computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest proble
Graph bandwidth
In graph theory, the graph bandwidth problem is to label the n vertices vi of a graph G with distinct integers so that the quantity is minimized (E is the edge set of G).The problem may be visualized
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MAXEkSAT is a problem in computational complexity theory that is a maximization version of the Boolean satisfiability problem 3SAT. In MAXEkSAT, each clause has exactly k literals, each with distinct
Metric k-center
In graph theory, the metric k-center or metric facility location problem is a combinatorial optimization problem studied in theoretical computer science. Given n cities with specified distances, one w
Radio coloring
In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels to the graphssuch that the labels of adjacent
MAX-3SAT is a problem in the computational complexity subfield of computer science. It generalises the Boolean satisfiability problem (SAT) which is a decision problem considered in complexity theory.
Quadratic assignment problem
The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics, from the category of the facil
Closest string
In theoretical computer science, the closest string is an NP-hard computational problem, which tries to find the geometrical center of a set of input strings. To understand the word "center", it is ne
MAX-3LIN-EQN is a problem in Computational complexity theory where the input is a system of linear equations (modulo 2). Each equation contains at most 3 variables. The problem is to find an assignmen
Minimum-weight triangulation
In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge length. That is, an input polygon or the convex
Rectilinear Steiner tree
The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem (MRST), or rectilinear Steiner minimum tree problem (RSMT) is a variant of the geometric Steiner tree problem in the plan
Graph coloring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest
Quadratic bottleneck assignment problem
In mathematics, the quadratic bottleneck assignment problem (QBAP) is one of fundamental combinatorial optimization problems in the branch of optimization or operations research, from the category of
Minimum relevant variables in linear system
MINimum Relevant Variables in Linear System (Min-RVLS) is a problem in mathematical optimization. Given a linear program, it is required to find a feasible solution in which the number of non-zero var
Rectangle packing
Rectangle packing is a packing problem where the objective is to determine whether a given set of small rectangles can be placed inside a given large polygon, such that no two small rectangles overlap