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Graduate
By
Shiva Kintali
on June 17, 2012 | Updated Dec. 6, 2017
Vertex cover using DFS
Consider the following algorithm for Vertex Cover of a graph \(G\) : Run depth first search (DFS) on \(G\). Output the vertices which are not leaves in the DFS tree. Prove the following : The ou…
Computer Science
Mathematics
Approximation Algorithms
Graph Theory
vertex cover
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Graduate
By
Shiva Kintali
on Aug. 8, 2012 | Updated Dec. 6, 2017
Gallai Identities
Consider the following parameters of an undirected graph \(G\) on \(n\) vertices. \(\nu(G)\) is the size of a maximum matching of \(G\). \(\tau(G)\) is the size of a minimum vertex cover of \(G\). …
Mathematics
Graph Theory
edge cover
independent set
matching
vertex cover
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Undergraduate
By
Shiva Kintali
on June 8, 2012 | Updated Dec. 6, 2017
Linear time algorithms on trees
Let \(T(V,E)\) be a tree. Design linear time (i.e., \(O(|V|)\) time) algorithms for the following problems : Find an optimal vertex cover in \(T\). Find a maximum matching in \(T\). Find a maximum i…
Computer Science
Mathematics
Algorithms
Graph Theory
independent set
linear time algorithms
matching
trees
vertex cover
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Graduate
By
Shiva Kintali
on Sept. 11, 2012 | Updated Dec. 6, 2017
Vertex cover in bipartite graphs
The Vertex Cover of a graph \(G(V,E)\) is a set of vertices \(S \subseteq V\) such that each edge of the graph is incident to at least one vertex of the set \(S\). Minimum cost vertex cover : Given a…
Mathematics
Optimization
Graph Theory
Linear Programming
bipartite graph
vertex cover
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Graduate
By
Shiva Kintali
on June 7, 2012 | Updated Dec. 6, 2017
Fixed-parameter tractability of Vertex Cover
Let \(G(V,E)\) be an undirected graph. A subset \(S \subseteq V\) is a vertex cover of \(G\) if every edge has at least one end point in \(V\). Design an \(O(|V|{\cdot}k + k^2{2^k})\) time algorithm t…
Computer Science
Algorithms
fpt algorithms
vertex cover
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