Independent Set (graph Theory)
In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent. That is, it is a set I of vertices such that for every two vertices in I, there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in I. The size of an independent set is the number of vertices it contains.
A maximal independent set is an independent set such that adding any other vertex to the set forces the set to contain an edge.
A maximum independent set is a largest independent set for a given graph G and its size is denoted α(G). The problem of finding such a set is called the maximum independent set problem and is an NP-hard optimization problem. As such, it is unlikely that there exists an efficient algorithm for finding a maximum independent set of a graph.
Read more about Independent Set (graph Theory): Properties, Finding Independent Sets, Software For Searching Maximum Independent Set, Software For Searching Maximal Independent Set
Famous quotes containing the words independent and/or set:
“We are independent of the change we detect. The longer the lever, the less perceptible its motion. It is the slowest pulsation which is the most vital. The hero then will know how to wait, as well as to make haste. All good abides with him who waiteth wisely; we shall sooner overtake the dawn by remaining here than by hurrying over the hills of the west.”
—Henry David Thoreau (1817–1862)
“The extra worry began it—on the
Blue blue mountain—she never set foot
And then and there. Meanwhile the host
Mourned her quiet tenure. They all stayed chatting.
No one did much about eating.”
—John Ashbery (b. 1927)