Connected bin packing problem on traceable graphs

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 ۲ 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 ۲.

Keywords:

Bin Packing Problem , Connectivity , Complexity theory , Approximation Algorithms