counting problem
counting problem
1. The task of finding the number of elements of some set with a particular property. Such counting problems are usually encountered in combinatorics.
2. The task of counting the number of solutions to a problem. For example, to find the number of spanning trees of a given graph, there is a formula in terms of the determinant of a certain matrix that is computable in polynomial time. However there are other problems, like counting the number of Hamiltonian cycles in a given graph, that are expected to be difficult, because determining whether or not a graph has a Hamiltonian cycle is NP-complete (see P=NP question). Although it is possible to determine whether or not a graph has a perfect matching (a set of edges that do not meet each other but meet every vertex) in polynomial time, computing the number of such matchings can be done in polynomial time only if P=NP.
The matching problem referred to is, in the bipartite case, the same as computing the permanent of a 0–1 matrix, for which no good methods are known.
1. The task of finding the number of elements of some set with a particular property. Such counting problems are usually encountered in combinatorics.
2. The task of counting the number of solutions to a problem. For example, to find the number of spanning trees of a given graph, there is a formula in terms of the determinant of a certain matrix that is computable in polynomial time. However there are other problems, like counting the number of Hamiltonian cycles in a given graph, that are expected to be difficult, because determining whether or not a graph has a Hamiltonian cycle is NP-complete (see P=NP question). Although it is possible to determine whether or not a graph has a perfect matching (a set of edges that do not meet each other but meet every vertex) in polynomial time, computing the number of such matchings can be done in polynomial time only if P=NP.
The matching problem referred to is, in the bipartite case, the same as computing the permanent of a 0–1 matrix, for which no good methods are known.
More From encyclopedia.com
Natural Numbers , The natural numbers are the ordinary numbers, 1, 2, 3,. . . with which humans count. Sometimes they are called the counting numbers. Natural numbers… Platelets , Definition
A platelet count is a diagnostic test that determines the number of platelets in the patient's blood. Platelets, which are also called thr… Problem Solving , A managerial problem can be described as the gap between a given current state of affairs and a future desired state. Problem solving may then be tho… George S. Counts , Progressive educator, sociologist, and political activist, George S. Counts challenged teachers and teacher educators to use school as a means for cr… Algorithm , An algorithm is any well-defined procedure for solving a given class of problems. Ideally, when applied to a particular problem in that class, the al… Addition , Addition, indicated by a + sign, is a method of combining numbers. The result of adding two numbers is called their sum.
Adding natural numbers
Consi…
You Might Also Like
NEARBY TERMS
counting problem