-
Inf. Process. Lett. 01/2012; 112:218-222.
-
Theor. Comput. Sci. 01/2004; 321:405-414.
-
Algorithms - ESA 2003, 11th Annual European Symposium, Budapest, Hungary, September 16-19, 2003, Proceedings; 01/2003
-
Algorithm Theory - SWAT 2002, 8th Scandinavian Workshop on Algorithm Theory, Turku, Finland, July 3-5, 2002 Proceedings; 01/2002
-
[show abstract]
[hide abstract]
ABSTRACT: We consider the problem of finding the longest increasing subsequence in a sliding window over a given sequence (LISW). We propose an output-sensitive data structure that solves this problem in time for a sequence of n elements. This data structure substantially improves over the naı̈ve generalization of the longest increasing subsequence algorithm and in fact produces an output-sensitive optimal solution.
Theoretical Computer Science.
-
[show abstract]
[hide abstract]
ABSTRACT: We consider the problem of sorting a permutation using a network of data structures as introduced by Knuth and Tarjan. In general the model as considered previously was restricted to networks that are directed acyclic graphs (DAGs) of stacks and/or queues. In this paper we study the question of which are the smallest general graphs that can sort an arbitrary permutation and what is their efficiency. We show that certain two-node graphs can sort in time Θ(n2) and no simpler graph can sort all permutations. We then show that certain three-node graphs sort in time Ω(n3/2), and that there exist graphs of k nodes which can sort in time Θ(nlogkn), which is optimal.
Discrete Applied Mathematics.
