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

Kehong Wang

doi:10.1117/12.2673307

14 April 2023 Approximation algorithms for variable-sized materials constructing tree-form structures in undirected graph

Kehong Wang

Author Affiliations +

Proceedings Volume 12613, International Conference on Computer Vision, Application, and Algorithm (CVAA 2022); 1261313 (2023) https://doi.org/10.1117/12.2673307
Event: International Conference on Computer Vision, Application, and Algorithm (CVAA 2022), 2022, Chongqing, China

Abstract

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 graph G = (V, E; w; b), a tree-form structure S and some pieces of m types of materials, where w : E → R⁺ is a length function , b : E → R⁺ is a cost function , we will attempt to construct a subgraph G' from G , having the structure S , 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 S is a spanning tree, we design a two- approximation algorithm to solve the problem of variable-sized materials constructing spanning tree. (2) When the structure S is a single-source shortest paths tree, we design a two- approximation algorithm to solve the problem of variable-sized materials constructing single-source shortest paths tree.

Citation Download Citation

Kehong Wang "Approximation algorithms for variable-sized materials constructing tree-form structures in undirected graph", Proc. SPIE 12613, International Conference on Computer Vision, Application, and Algorithm (CVAA 2022), 1261313 (14 April 2023); https://doi.org/10.1117/12.2673307

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KEYWORDS

Algorithm development

Algorithms

Design and modelling

Mathematical optimization

Fiber optic networks

Transportation

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