2,717 research outputs found
Sorting with Complete Networks of Stacks
Knuth introduced the problem of sorting with a sequence of stacks. Tarjan extended this idea to sorting with acyclic networks of stacks (and queues), where items to be sorted move from a source through the network to a sink while they may be stored temporarily at nodes (the stacks). Both characterized which permutations are sortable; but complexity of sorting was not an issue
Average-Case Complexity of Shellsort
We prove a general lower bound on the average-case complexity of Shellsort:
the average number of data-movements (and comparisons) made by a -pass
Shellsort for any incremental sequence is \Omega (pn^{1 + 1/p) for all . Using similar arguments, we analyze the average-case complexity
of several other sorting algorithms.Comment: 11 pages. Submitted to ICALP'9
2-stack pushall sortable permutations
In the 60's, Knuth introduced stack-sorting and serial compositions of
stacks. In particular, one significant question arise out of the work of Knuth:
how to decide efficiently if a given permutation is sortable with 2 stacks in
series? Whether this problem is polynomial or NP-complete is still unanswered
yet. In this article we introduce 2-stack pushall permutations which form a
subclass of 2-stack sortable permutations and show that these two classes are
closely related. Moreover, we give an optimal O(n^2) algorithm to decide if a
given permutation of size n is 2-stack pushall sortable and describe all its
sortings. This result is a step to the solve the general 2-stack sorting
problem in polynomial time.Comment: 41 page
On the least exponential growth admitting uncountably many closed permutation classes
We show that the least exponential growth of counting functions which admits
uncountably many closed permutation classes lies between 2^n and
(2.33529...)^n.Comment: 13 page
Data Structures Lecture Notes (Student Version)
Lecture notes for a data-structures course in computer science with examples in Java. Students in this course should have already taken an intro-programming course in an object-oriented language and have a basic grasp of Java. These are not designed to accompany any specific textbook
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