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Independent set problem - Description | | Independent set problem - Description: Encyclopedia II - Independent set problem - Description | | Given a graph G, an independent set is a subset of its vertices that are pairwise not adjacent. In other words, the subgraph induced by these vertices has no edges, only isolated vertices. Then, the independent set problem asks if, given a graph G and an integer k, does G have an independent set of size at least k?
The corresponding optimization problem is the maximum independent set problem, which attempts to find the largest independent set in a graph. Given a solution to the decision ...
See also:Independent set problem, Independent set problem - Description, Independent set problem - Algorithms, Independent set problem - Proof of NP-completeness | | | Independent set problem, Independent set problem - Algorithms, Independent set problem - Description, Independent set problem - Proof of NP-completeness | | |
| | | Independent set problem: Encyclopedia II - Independent set problem - Description
Independent set problem - Description
Given a graph G, an independent set is a subset of its vertices that are pairwise not adjacent. In other words, the subgraph induced by these vertices has no edges, only isolated vertices. Then, the independent set problem asks if, given a graph G and an integer k, does G have an independent set of size at least k?
The corresponding optimization problem is the maximum independent set problem, which attempts to find the largest independent set in a graph. Given a solution to the decision problem, binary search can be used to solve this problem with O(log |V|) invocations of that solution. This problem is known to have no constant-factor approximation algorithm unless P=NP.
Other related archivesNP-complete, approximation algorithm, binary search, boolean satisfiability problem, brute force, combinatorics, conjunctive normal form, graph, graph coloring problem, graph theory, independent set, mathematics, optimization problem, polynomial-time many-one reduction
 Adapted from the Wikipedia article "Description", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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