  The smooth heap is a recently introduced self-adjusting heap [Kozma,
Saranurak, 2018] similar to the pairing heap [Fredman, Sedgewick, Sleator,
Tarjan, 1986]. The smooth heap was obtained as a heap-counterpart of Greedy
BST, a binary search tree updating strategy conjectured to be
\emph{instance-optimal} [Lucas, 1988], [Munro, 2000]. Several adaptive
properties of smooth heaps follow from this connection; moreover, the smooth
heap itself has been conjectured to be instance-optimal within a certain class
of heaps. Nevertheless, no general analysis of smooth heaps has existed until
now, the only previous analysis showing that, when used in \emph{sorting mode}
($n$ insertions followed by $n$ delete-min operations), smooth heaps sort $n$
numbers in $O(n\lg n)$ time.
  In this paper we describe a simpler variant of the smooth heap we call the
\emph{slim heap}. We give a new, self-contained analysis of smooth heaps and
slim heaps in unrestricted operation, obtaining amortized bounds that match the
best bounds known for self-adjusting heaps. Previous experimental work has
found the pairing heap to dominate other data structures in this class in
various settings. Our tests show that smooth heaps and slim heaps are
competitive with pairing heaps, outperforming them in some cases, while being
comparably easy to implement.
