Iranian Journal of Numerical Analysis and Optimization (Mar 2022)

Connected bin packing problem on traceable graphs

  • A. Nejoomi,
  • A. Dolati

DOI
https://doi.org/10.22067/ijnao.2021.67913.1010
Journal volume & issue
Vol. 12, no. 1
pp. 163 – 171

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.

Keywords