Computational geometry: an introduction
Computational geometry: an introduction
Discrete Applied Mathematics
Finding a 2-Core of a Tree in Linear Time
SIAM Journal on Discrete Mathematics
Maintaining Center and Median in Dynamic Trees
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Finding Cores of Limited Length
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Core and Conditional Core Path of Specified Length in Special Classes of Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
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In this paper, we study the problem of locating a median path of limited length on a tree under the condition that some existing facilities are already located. The existing facilities may be located at any subset of vertices. Upper and lower bounds are proposed for both the discrete and continuous models. In the discrete model, a median path is not allowed to contain partial edges. In the continuous model, a median path may contain partial edges. The proposed upper bounds for these two models are O(nlog n) and O(nlog n驴(n)), respectively. They improve the previous ones from O(nlog2 n) and O(n2), respectively. The proposed lower bounds are both 驴(nlog n). The lower bounds show that our upper bound for the discrete model is optimal and the margin for possible improvement on our upper bound for the continuous model is slim.