
The queuenumber of planar posets
Heath and Pemmaraju conjectured that the queuenumber of a poset is boun...
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On the QueueNumber of Partial Orders
The queuenumber of a poset is the queuenumber of its cover graph viewe...
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An Elementary Proof of the 3 Dimensional Simplex Mean Width Conjecture
After a Hessian computation, we quickly prove the 3D simplex mean width ...
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The queuenumber of posets of bounded width or height
Heath and Pemmaraju conjectured that the queuenumber of a poset is boun...
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On the Queue Number of Planar Graphs
A kqueue layout is a special type of a linear layout, in which the line...
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Tight Approximation for Unconstrained XOS Maximization
A set function is called XOS if it can be represented by the maximum of ...
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Improved queuesize scaling for inputqueued switches via graph factorization
This paper studies the scaling of the expected total queue size in an n×...
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Lazy Queue Layouts of Posets
We investigate the queue number of posets in terms of their width, that is, the maximum number of pairwise incomparable elements. A longstanding 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 socalled lazy linear extension. We extend and thoroughly analyze lazy linear extensions for posets of width w > 2. Our analysis implies an upper bound of (w1)^2 +1 on the queue number of widthw posets, which is tight for the strategy and yields an improvement over the previously bestknown bound. Further, we provide an example of a poset that requires at least w+1 queues in every linear extension, thereby disproving the conjecture for posets of width w > 2.
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