The -maxian problem on a tree

Burkard, Rainer E.; Fathali, Jafar; Kakhki, Hossein Taghizadeh

doi:10.1016/j.orl.2006.03.016

Cited by 21 publications

(5 citation statements)

References 9 publications

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“…Burkard et al [3] showed that the solution of the 2-maxian problem is two end vertices of a diameter which can be obtained in a linear time. For λ ∈ [0, 1] the balanced 2-maxian problem also could be solved by such edge deletion method as in Burkard et al [4] which is presented for the 2-median problem on a tree with positive and negative weights.…”

Section: Balanced 2-maxian Problem On a Treementioning

confidence: 99%

“…They presented an O(mn log n) time algorithm, and Tamir [20] improved the time complexity to O(mn). Burkard et al [3] showed that the optimal solution of the 2-maxian problem on a tree lies on the two end vertices of the diameter, where diameter is the longest path of the tree. They also showed that pmaxian problem on the tree is reduced to the 2-maxian.…”

Section: Introductionmentioning

confidence: 99%

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The balanced 2-median and 2-maxian problems on a tree

Fathali¹,

Zaferanieh²

2018

Preprint

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This paper deals with the facility location problems with balancing on allocation clients to servers. Two bi-objective models are considered, in which one objective is the traditional p-median or p-maxian objective and the second is to minimize the maximum demand volume allocated to any facility. An edge deletion method with time complexity O(n 2 ) is presented for the balanced 2-median problem on a tree. For the balanced 2-maxian problem, it is shown the optimal solution is two end vertices of the diameter of the tree, which can be obtained in a linear time.

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Section: Balanced 2-maxian Problem On a Treementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The balanced 2-median and 2-maxian problems on a tree

Fathali¹,

Zaferanieh²

2018

Preprint

Self Cite

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“…If the aim is to maximize the total maximum weighted distances from all customers to p new facilities, the corresponding problem is the so-called p-maxian problem. The p-maxian problem was first considered by Burkard et al [11], who showed that the problem could be solved in linear time. Kang and Cheng [12] presented a linear time algorithm for the p-maxian problem on block graphs, where each block graph is a super class of tree graphs.…”

Section: Introductionmentioning

confidence: 99%

The Constrained 2-Maxian Problem on Cycles

Bai,

2024

Mathematics

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This paper deals with p-maxian problem on cycles with an upper bound on the distances of all facilities. We consider the case of p=2 and show that, in the worst case, the optimal solution contains at least one vertex of the underlying cycle, which helps to develop an efficient algorithm to solve the constrained 2-maxian problem. Based on this property, we develop a linear time algorithm for the constrained 2-maxian problem on a cycle. We also discuss the relations between the constrained and unconstrained 2-maxian problems on which the underlying graphs are cycles.

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“…Bài toán này được gọi là bài toán p-maxian trên cây, tham khảo Burkard et al (2007). Với 1 p = , bài toán sẽ là bài toán 1-maxian và nó có thể được giải trong thời gian tuyến tính bởi Ting (1984).…”

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“…Với 1 p = , bài toán sẽ là bài toán 1-maxian và nó có thể được giải trong thời gian tuyến tính bởi Ting (1984). Với 1 p > , Burkard et al (2007) chỉ ra rằng hai đỉnh đầu mút của đường đi dài nhất trên cây là 2-maxian của T và p-maxian sẽ chứa 2-maxian. Do đó, bài toán pmaxian có thể được giải trong thời gian tuyến tính bằng cách tìm đường đi dài nhất trên cây.…”

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