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https://en.wikipedia.org/wiki/Vertex_cover
In the mathematical discipline of graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The problem of finding a minimum vertex cover is a classical optimization problem in computer science and is a typical example of an NP-hard optimization problem that has an approximation algorithm.
http://www.isca.in/COM_IT_SCI/Archive/v1/i6/2.ISCA-RJCITS-2013-028.pdf
Minimum vertex cover is focus point for researchers since last decade due to its vast areas of application. In this research paper we have presented a modified form of approximation algorithm for minimum vertex cover which makes use of data structure proposed already named vertex support.
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.310.7383
CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The Minimum Vertex Cover (MVC) problem is a classic graph optimization NP- complete problem. In this paper a competent algorithm, called Vertex Support Algorithm (VSA), is designed to find the smallest vertex cover of a graph. The VSA is tested on a large number of random graphs and DIMACS benchmark graphs.
http://www.dharwadker.org/vertex_coloring/
We present a new polynomial-time algorithm for finding proper m-colorings of the vertices of a graph.We prove that every graph with nvertices and maximum vertex degree Δ must have chromatic number χ(G) less than or equal to Δ+1 and that the algorithm will always find a proper m-coloring of the vertices of Gwith mless than or equal to Δ+1.
https://www.researchgate.net/publication/258837345_Modified_Vertex_Support_Algorithm_A_New_approach_for_approximation_of_Minimum_vertex_cover
Another simple heuristic algorithm is the modified vertex support algorithm (MVSA) [11] which is achieved by modifying the vertex support algorithm [12]. The same data structure has been ...
http://reed.cs.depaul.edu/lperkovic/csc327/graphs/graphs.html
which is adjacent from any vertex/node in the tree built so far; and; which has the lowest weight among alternatives (i.e., all edges connected from any vertex/node in the tree built so far). Algorithm: Let G = (V, E) which is represented by an adjacency list Adj. Some support data structures:
https://thesai.org/Downloads/Volume7No3/Paper_9-NMVSA_Greedy_Solution_for_Vertex_Cover_Problem.pdf
The algorithm starts by finding the degree of each vertex not yet selected in the vertex cover. The degree of the vertex is the number of adjacent neighbors for vertex. The second stage after finding the degrees is finding the support value for each vertex. The algorithm proceeds by finding a list that contains
https://bradfieldcs.com/algos/graphs/dijkstras-algorithm/
Dijkstra’s Algorithm. The algorithm we are going to use to determine the shortest path is called “Dijkstra’s algorithm.” Dijkstra’s algorithm is an iterative algorithm that provides us with the shortest path from one particular starting node to all other nodes in the graph. Again this is similar to the results of a breadth first search.
http://tandy.cs.illinois.edu/dartmouth-cs-approx.pdf
Now, let us consider an approximation algorithm for NP-Hard problem, Vertex Cover. 1.2 Approximation Algorithm for Vertex Cover Given a G = (V,E), find a minimum subset C ⊆V, such that C “covers” all edges in E, i.e., every edge ∈E is incident to at least one vertex in …
https://www.researchgate.net/publication/228978402_A_Simple_Algorithm_to_Optimize_Maximum_Independent_Set
A Simple Algorithm to Optimize Maximum Independent Set. ... In this paper an efficient algorithm, called Vertex Support Algorithm (VSA), is designed to find the maximum independent set of a graph ...
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