19 research outputs found
A Cover-Merging-Based Algorithm for the Longest Increasing Subsequence in a Sliding Window Problem
A longest increasing subsequence problem (LIS) is a well-known combinatorial problem with applications mainly in bioinformatics, where it is used in various projects on DNA sequences. Recently, a number of generalisations of this problem were proposed. One of them is to find an LIS among all fixed-size windows of the input sequence (LISW). We propose an algorithm for the LISW problem based on cover representation of the sequence that outperforms the existing methods for some class of the input sequences
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
Longest increasing subsequences in windows based on canonical antichain partition
Given a sequence Ļ1Ļ2... Ļn, a longest increasing subsequence (LIS) in a window Ļā©l, rāŖ = ĻlĻl+1... Ļr is a longest subsequence Ļ = Ļi1Ļi2... ĻiT such that l ā¤ i1 < i2 < Ā· Ā· Ā· < iT ā¤ r and Ļi1 < Ļi2 < Ā· Ā· Ā· < ĻiT. We consider the Lisw problem, which is to find the longest increasing subsequences in a sliding window of fixed-size w over a sequence. Formally, it is to find a LIS for every window in a set SFIX = ļæ½ Ļā©i + 1, i + w āŖ ļæ½ ļæ½ 0 ā¤ i ā¤ n ā w ļæ½ āŖ ļæ½ Ļā©1, iāŖ, Ļā©n ā i, n āŖ ļæ½ ļæ½ i < w ļæ½. By maintaining a canonical antichain partition in windows, we present an optimal output-sensitive algorithm to solve this problem in O(output) time, where output is the sum of the lengths of the n+w ā1 LISs in those windows of SFIX. In addition, we propose a more generalized problem called Lisset problem, which is to find a LIS for every window in a set SVAR containing variable-size windows. By applying our algorithm, we provide an efficient solution for the Lisset problem to output a LIS (or all the LISs) in every window which is better than the straightforward generalization of classical LIS algorithms. An upper bound of our algorithm on the Lisset problem is discussed
Longest increasing subsequences in windows based on canonical antichain partition
AbstractGiven a sequence Ļ1Ļ2ā¦Ļn, a longest increasing subsequence (LIS) in a window Ļćl,rć=ĻlĻl+1ā¦Ļr is a longest subsequence Ļ=Ļi1Ļi2ā¦ĻiT such that lā¤i1<i2<āÆ<iTā¤r and Ļi1<Ļi2<āÆ<ĻiT. We consider the LiswĀ problem, which is to find the longest increasing subsequences in a sliding window of fixed-size w over a sequence. Formally, it is to find a LIS for every window in a set SFIX={Ļći+1,i+wćā£0ā¤iā¤nāw}āŖ{Ļć1,ić,Ļćnāi,nćā£i<w}. By maintaining a canonical antichain partition in windows, we present an optimal output-sensitive algorithm to solve this problem in O(output) time, where output is the sum of the lengths of the n+wā1 LISs in those windows of SFIX. In addition, we propose a more generalized problem called LissetĀ problem, which is to find a LIS for every window in a set SVAR containing variable-size windows. By applying our algorithm, we provide an efficient solution for the LissetĀ problem to output a LIS (or all the LISs) in every window which is better than the straightforward generalization of classical LIS algorithms. An upper bound of our algorithm on the LissetĀ problem is discussed
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)
The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), SaarbrĀØucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), WĀØurzburg (1993), Caen (1994), MĀØunchen (1995), Grenoble (1996), LĀØubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..