Connected bin packing problem on traceable graphs

َAhmad Nejoomi | Ardeshir Dolati

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=159572
Date :  2022/03/01
Publish in :    Iranian Journal of Numerical Analysis and Optimization
DOI :  https://doi.org/10.22067/IJNAO.2021.67913.1010
Link :  https://ijnao.um.ac.ir/article_40635_e5f368461d145a66208acf1635aeba83.pdf
Keywords :Bin Packing Problem, Connectivity, Complexity Theory, Approximation Algorithms

Abstract :

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We consider a new extension of the bin packing problem in which a set of connectivity constraints should be satisfied. An undirected graph with a weight function on the nodes is given. The objective is to pack all the nodes in the minimum number of unit-capacity bins, such that the induced subgraph on the set of nodes packed in each bin is connected. After analyzing some structural properties of the problem, we present a linear time approximation algorithm for this problem when the underlying graph is traceable. We show that the approximation factor of this algorithm is 2 and this factor is tight. Finally, concerning the investigated structural properties, we extend the algorithm for more general graphs. This extended algorithm also has a tight approximation factor of 2.