Polynomial algorithms to finite Veber problem for a tree network

Panyukov, Anatoly V.; Pelzwerger, Boris V.

doi:10.1016/0377-0427(91)90215-6

Cited by 9 publications

(5 citation statements)

References 4 publications

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“…To introduce the notation and simplify the presentation of main paper results, we give the algorithm for Weber problem from the author's work [5].…”

Section: Algorithm Of Solving Weber Problem For a Tree Networkmentioning

confidence: 99%

“…presents unambiguous maps) then problem Θ is known as Weber problem for a tree-connecting network. To solve this problem the polynomial algorithm [5] of complexity O(|J||V | 2 ) is used.…”

Section: Introductionmentioning

confidence: 99%

“…(4) The optimal solution of Weber problem is equal to min u∈V [c(N, u)]. The computing complexity of algorithm TreeVebPrbAlg is O(|J||V | 2 ).For more details and proofs see[5].…”

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confidence: 99%

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On the Existence of an Integer Solution of the Relaxed Weber Problem for a Tree Network

Panyukov¹

2019

Bulletin of the SUSU. MMP

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The problem of finding the optimal arrangement of vertices of a tree network in the installation space representing a finite set is considered. The criterion of optimality is the minimization of the total cost of deployment and the cost of communications. Placement of different tree vertices in one point of the installation space is allowed. This problem is known as Weber problem for a tree network. The statement of Weber problem as an integer linear programming problem is given in this research. It's proved that a set of optimal solutions of corresponding relaxed Weber problem for a tree-network contains the integer solution. This fact allows to prove the existence a saddle point while proving the performance of decomposition algorithms for problems different from problems because of additional restrictions.

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“…To introduce the notation and simplify the presentation of main paper results, we give the algorithm for Weber problem from the author's work [5].…”

Section: Algorithm Of Solving Weber Problem For a Tree Networkmentioning

confidence: 99%

“…presents unambiguous maps) then problem Θ is known as Weber problem for a tree-connecting network. To solve this problem the polynomial algorithm [5] of complexity O(|J||V | 2 ) is used.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Existence of an Integer Solution of the Relaxed Weber Problem for a Tree Network

Panyukov¹

2019

Bulletin of the SUSU. MMP

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“…Во-вторых: структура n-сложной цепи Маркова представляет собой n-последовательносвязную цепь, вследствие чего возможно использование n-последовательносвязных цепей в построении эффективных алгоритмов для решения задач выбора оптимального поведения в системах, описываемых управляемыми марковскими процессами, когда цепь Маркова является n-сложной. В-третьих древовидная ширина [1] некоторых частных случаев n-последовательносвязного графа равна n+1, вследствие чего представляется перспективным использование некоторых частных случаев n-последовательносвязного графа в построении эффективных приближенных c 2013 Шангин Р. Э. квазиполиномиальных алгоритмов, использующих идею динамического программирования, для решения ряда N P -трудных задач, в частности задачи Вебера в дискретной постановке [2,6,9] и квадратичной задачи о назначениях [3].…”

Section: Introductionunclassified

Constructive descriptions of n-sequentially connected graphs

Shangin¹

2013

Владикавказский Математический Журнал

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Вводится класс n-последовательносвязных графов, рассматриваются области их применения. Приводятся основные характеристики и свойства графов рассматриваемого класса. Определяются отношения класса n-последовательносвязных графов к классам совершенных, триангулированных, полных и расщепляемых графов.

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“…Problem (12.1) is a special case of the polynomially solvable Weber problem on a tree network [8]. Let us give a sketch of the chain adaptation of the algorithm from [9] for the purpose of presentation completeness. Let us locate the vertex c 0 ∈ V(C) at the vertex v 0 ∈ V(G).…”

Section: Calculation Of λ(λ)mentioning

confidence: 99%