We consider the two-bar charts packing problem generalizing the strongly NP-hard bin packing problem. We prove that the problem remains strongly NP-hard even if each two-bar chart has at least one bar higher than 1/2. If the first (or second) bar of each two-bar chart is higher than 1/2, we show that the O(n 2 )-time greedy algorithm with lexicographic ordering of two-bar charts constructs a packing of length at most OPT +1, where OPT is optimum, and present an O(n 2.5 )-time algorithm that constructs a packing of length at most 4/3 • OPT +2/3 in the NP-hard case where each two-bar chart has at least one bar higher than 1/2. Bibliography: 22 titles. Illustrations: 2 figures.
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