Solving the shortest-paths problem on bipartite permutation graphs efficiently
Information Processing Letters
Efficient algorithms for finding a core of a tree with a specified length
Journal of Algorithms
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Finding Cores of Limited Length
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
The Conditional Location of a Median Path
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Discrete Applied Mathematics
Conditional location of path and tree shaped facilities on trees
Journal of Algorithms
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A core path of a graph is a path P in G that minimizes d (P ) = ${\underset{v \in V}{\sum}} d(v,P)w(v)$. In this paper, we study the location of core path of specified length in special classes of graphs. Further, we extend our study to the problem of locating a core path of specified length under the condition that some existing facilities are already located (known as conditional core path of a graph). We study both the problems stated above in vertex weighted bipartite permutation graphs, threshold graphs and proper interval graphs and give polynomial time algorithms for the core path and conditional core path problem in these classes. We also establish the NP-Completeness of the above problems in the same classes of graphs when arbitrary positive weights are assigned to edges.