Affiliation:
1. Department of Computer Engineering and Systems, Alexandria University, Egypt
Abstract
We give a variant of the pairing heaps that achieves the following amortized costs:
O
(1) per
find-min
and
insert
,
O
(log log
n
) per
decrease-key
and
meld
,
O
(log
n
) per
delete-min
; where
n
is the number of elements in the resulting heap on which the operation is performed. These bounds are the best known for any self-adjusting heap and match two lower bounds, one established by Fredman and the other by Iacono and Özkan, for a family of self-adjusting heaps that generalizes the pairing heaps but do not include our variant. We further show how to reduce the amortized cost for
meld
to be paid by the other operations, on the expense of increasing that of
delete-min
to
O
(log
n
+ log log
N
), where
N
is the total number of elements in the collection of heaps of the data structure (not just the heap under consideration by the operation).
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)