Three-Bar Charts Packing Problem

Three-Bar Charts Packing Problem is to pack the bar charts consisting of three bars each into the horizontal unit-height strip of minimal length. The bars of each bar chart may move vertically within the strip, but it is forbidden to change the order and separate the bars. For this novel issue, which is a generalization of the strongly NP-hard Two-Bar Charts Packing Problem considered earlier, we propose several approximation algorithms with guaranteed accuracy.