An Optimal Algorithm to Solve 2-Neighbourhood Covering Problem on Interval Graphs

Sukumar Mondal, Madhumangal Pal, Tapan K. Pal
2002 International Journal of Computer Mathematics  
Let G = (V, E) be a simple graph and k be a fixed integer. A vertex z is said to be a k-neighbourhood-cover of an edge (x, y) if d(x, z) ≤ k and d(y, z) ≤ k, where d(x, y) represents the distance between two vertices x and y. A set C ⊂ V is called a k-neighbourhood-covering set if every edge in E is k-neighbourhood-cover by some vertices of C. This problem is NP-complete for general graphs even it remains NP-complete for chordal graphs. Using dynamic programming technique, an O(n) time
more » ... O(n) time algorithm is designed to solve minimum 2-neighbourhood-covering problem on trapezoid graph. The trapezoid interval tree rooted at the vertex n is used to solve this problem.
doi:10.1080/00207160211921 fatcat:7uxq2ayodbhljjc6nicql6nh2i