## Mercurial > repos > shellac > sam_consensus_v3

### view env/lib/python3.9/site-packages/networkx/algorithms/approximation/independent_set.py @ 0:4f3585e2f14b draft default tip

Find changesets by keywords (author, files, the commit message), revision
number or hash, or revset expression.

"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

author | shellac |
---|---|

date | Mon, 22 Mar 2021 18:12:50 +0000 |

parents | |

children |

line wrap: on

line source

r""" Independent Set 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 maximum independent set is a largest independent set for a given graph G and its size is denoted $\alpha(G)$. 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. `Wikipedia: Independent set <https://en.wikipedia.org/wiki/Independent_set_(graph_theory)>`_ Independent set algorithm is based on the following paper: $O(|V|/(log|V|)^2)$ apx of maximum clique/independent set. Boppana, R., & Halldórsson, M. M. (1992). Approximating maximum independent sets by excluding subgraphs. BIT Numerical Mathematics, 32(2), 180–196. Springer. doi:10.1007/BF01994876 """ from networkx.algorithms.approximation import clique_removal __all__ = ["maximum_independent_set"] def maximum_independent_set(G): """Returns an approximate maximum independent set. Parameters ---------- G : NetworkX graph Undirected graph Returns ------- iset : Set The apx-maximum independent set Notes ----- Finds the $O(|V|/(log|V|)^2)$ apx of independent set in the worst case. References ---------- .. [1] Boppana, R., & Halldórsson, M. M. (1992). Approximating maximum independent sets by excluding subgraphs. BIT Numerical Mathematics, 32(2), 180–196. Springer. """ iset, _ = clique_removal(G) return iset