Approximation algorithms for constructing some required structures in digraphs

Li, Jianping; Ge, Yu; He, Shuai; Lichen, Junran

doi:10.1016/j.ejor.2013.07.033

Cited by 4 publications

(1 citation statement)

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“…Li et al [12] first studied network construction problem with path and graph constraints. The model they researched are as follows: given a weighted directed graph ( , ; ) D V A w  and a special material of bounded length L , where :…”

Section: Introduction and Problem Descriptionmentioning

confidence: 99%

Approximation algorithms for variable-sized materials constructing tree-form structures in undirected graph

Wang

2023

International Conference on Computer Vision, Application, and Algorithm (CVAA 2022)

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It is known that one-dimensional variable-sized bin packing problem and network optimization problem are classical combinatorial optimization problems. Inspired by this, we consider a new problem of variable-sized materials constructing some tree-form structures in undirected graph, where all edges spliced in such a tree-form structure are assembled from some pieces of m types of materials. More precisely, that is defined as follows: given a weighted graphtree-form structure  and some pieces of m types of materials, where :b E R   is a cost function , we will attempt to construct a subgraph G from G , having the structure  , such that each edge in G is further constructed by given m types of materials , the new objective is to minimize the total cost to construct subgraph G , where the total cost is sum of the cost to purchase materials and the cost to construct all edges in such a subgraph .G For this new problem, we obtained the following two main results.(1)When the structure  is a spanning tree, we design a 2approximation algorithm to solve the problem of variable-sized materials constructing spanning tree. (2) When the structure  is a single-source shortest paths tree, we design a 2approximation algorithm to solve the problem of variablesized materials constructing single-source shortest paths tree.

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Section: Introduction and Problem Descriptionmentioning

confidence: 99%