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Heuristic Algorithm for finding Maximum Independent Set 1.0
File ID: 78605

Heuristic Algorithm for finding Maximum Independent Set 1.0
Download Heuristic Algorithm for finding Maximum Independent Set 1.0http://www.mathworks.comReport Error Link
License: Freeware
File Size: 10.0 KB
Downloads: 202
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Heuristic Algorithm for finding Maximum Independent Set 1.0 Description
Description: findMIS is an heuristic algorithm for solving Maximum Independent Set problem (MIS).
An independent set of a graph is a subset of vertices in which no two vertices are
adjacent. Given a set of vertices, the maximum independent set problem calls
for finding the independent set of maximum cardinality.

Algorithm run in O(n^2) time, where n is the number of vertices (worst case).
Experimentally: time = 8.1e-007*n^2 + 2.2e-005*n + 0.00012 seconds, (see screenshot)

The algorithm has been independently developped but is similar to:
Balaji, Swaminathan, Kannan, "A Simple Algorithm to Optimize
Maximum Independent Set", Advanced Modeling and Optimization, Volume 12, Number 1, 2010

The neighborhood of v is defined by N(v) ={u in V such that u is adjacent to v}
The DEGREE of a vertex v in V, denoted by deg(v) and is defined by the number of
neighbors of v.
The SUPPORT of a vertex v in V is defined by the sum of the degree of the vertices
which are adjacent to v, i.e., support(v) = s(v) = sum( deg(u) ) where u are all
vertices in N(v).

"AD" is the adjacency matrix. It must be of logical values!
"priority" is used to break the ties (parity) situations that occur when more than one maximum independent set can be selected. Consider for example the trivial case of two nodes connected by one edge: there are two possible maximum independent sets. By using priority you can decide which vertex has to selected first. Try for example:
x=findMIS(logical([0 1; 1 0]),[1 2]) %Higher priority to node 1
x=findMIS(logical([0 1; 1 0]),[2 1]) %Higher priority to node 2

x is an binary array where x(i)=1 if vertex i belongs to the Maximum independent set
and x(i)=0 if belongs to the Minimum vertex cover.

License: Freeware

Related: allvertices, Algorithm, Binary, heuristic, and is, 81e007n2 2b, adjacency matrix, adjacent, advanced modeling, Optimization, belongs, independently, binary array, break, but is, Selected, be of

O/S:BSD, Linux, Solaris, Mac OS X

File Size: 10.0 KB

Downloads: 202

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