A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
Improved complexity bounds for center location problems on networks by using dynamic data structures
SIAM Journal on Discrete Mathematics
An O(log*n) approximation algorithm for the asymmetric p-center problem
Journal of Algorithms
A linear-time algorithm for solving the center problem on weighted cactus graphs
Information Processing Letters
The Centdian subtree on tree networks
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Asymmetric k-center is log* n-hard to approximate
Journal of the ACM (JACM)
An improved algorithm for the p-center problem on interval graphs with unit lengths
Computers and Operations Research
Efficient algorithms for center problems in cactus networks
Theoretical Computer Science
Asymmetric k-center with minimum coverage
Information Processing Letters
Center location problems on tree graphs with subtree-shaped customers
Discrete Applied Mathematics
Note: A characterization of block graphs
Discrete Applied Mathematics
Conditional location of path and tree shaped facilities on trees
Journal of Algorithms
Optimal algorithms for the path/tree-shaped facility location problems in trees
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
A 1-center problem on the plane with uniformly distributed demand points
Operations Research Letters
Structured p-facility location problems on the line solvable in polynomial time
Operations Research Letters
A simple heuristic for the p-centre problem
Operations Research Letters
Hi-index | 5.23 |
Let G(V,E,w,l) denote an n-vertex and m-edge graph in which w is a function mapping each vertex v to a positive weight w(v) and l is a function mapping each edge e to a positive length l(e). Given a positive integer p, the p-Center problem involves finding a set Q with p vertices of G to be the locations for building facilities. The objective is to minimize the maximum weighted distance from each vertex in V-Q to its nearest vertex in Q. This paper considers a practical restriction: the induced subgraph of the selected p vertices must be connected. The new variant is called the Connected p-Center problem (the CpC problem). For each fixed integer t=1, on block graphs with exactly t blocks, we first show that the CpC problem is NP-hard when (1) w(v)=1, for all vertices v, and l(e)@?{1,2}, for all edges e, and (2) w(v)@?{1,2}, for all vertices v, and l(e)=1, for all edges e, respectively. Second, an O(n+m)-time algorithm for solving the CpC problem on block graphs with unit vertex-weights and unit edge-lengths is proposed. Then, the algorithmic result is extended to handle the situation in which some vertices in G cannot be included to form feasible solutions. The complexity of the extended algorithm is also O(n+m).