Browsing by Author Michael A., Bekos
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We investigate the queue number of posets in terms of their width, that is, the maximum number of pairwise incomparable elements. A long-standing conjecture of Heath and Pemmaraju asserts that every poset of width w has queue number at most w. The conjecture has been confirmed for posets of width w=2 via so-called lazy linear extension. We extend and thoroughly analyze lazy linear extensions for posets of width w>2. Our analysis implies an upper bound of (w−1)2+1 on the queue number of width-w posets, which is tight for the strategy and yields an improvement over the previously best-known bound. Further, we provide an example of a poset that requires at least w+1 queues in every linea... |
