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Weighted Shortest Common Supersequence Problem Revisited [chapter]

Panagiotis Charalampopoulos, Tomasz Kociumaka, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszyński, Tomasz Waleń, Wiktor Zuba
2019 Lecture Notes in Computer Science  
We revisit the Weighted Shortest Common Supersequence (WSCS) problem, introduced by Amir et al. [SPIRE 2011], that is, the SCS problem on weighted strings.  ...  We also discover a fundamental difference between the WSCS problem and the Weighted Longest Common Subsequence (WLCS) problem, introduced by Amir et al. [JDA 2010].  ...  A common supersequence of X and Y is a string S such that X and Y are both subsequences of S. A shortest common supersequence (SCS) of X and Y is a common supersequence of X and Y of minimum length.  ... 
doi:10.1007/978-3-030-32686-9_16 fatcat:anarfr4jfrhbziwm6cmeijveue

Weighted Shortest Common Supersequence Problem Revisited [article]

Panagiotis Charalampopoulos, Tomasz Kociumaka, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Juliusz Straszyński, Tomasz Waleń and Wiktor Zuba
2019 arXiv   pre-print
We revisit the Weighted Shortest Common Supersequence (WSCS) problem, introduced by Amir et al. [SPIRE 2011], that is, the SCS problem on weighted strings.  ...  We also discover a fundamental difference between the WSCS problem and the Weighted Longest Common Subsequence (WLCS) problem, introduced by Amir et al. [JDA 2010].  ...  A common supersequence of X and Y is a string S such that X and Y are both subsequences of S. A shortest common supersequence (SCS) of X and Y is a common supersequence of X and Y of minimum length.  ... 
arXiv:1909.11433v1 fatcat:wazrrs4fvfaw7jgtd53bbhvnoe

SUPERSEQUENCES OF MASKS FOR OLIGO-CHIPS

A. GUÉNOCHE
2004 Journal of Bioinformatics and Computational Biology  
Let T be a table such that T (i, j) is the length of a shortest supersequence common to prefixes µ [1, i] and ν [1, j] .  ...  As soon as the number of oligo words is greater than two, the shortest common supersequence problem, or SCS-problem, has been proved NP-Hard [Maier, 1978] , even for binary strings [Räihä and Ukkonen  ... 
doi:10.1142/s0219720004000685 pmid:15359421 fatcat:q5yh645oy5c7df5w3eer6kraze

A Comparison of Evolutionary Approaches to the Shortest Common Supersequence Problem [chapter]

Carlos Cotta
2005 Lecture Notes in Computer Science  
The Shortest Common Supersequence problem is a hard combinatorial optimization problem with numerous practical applications.  ...  The Shortest Common Supersequence Problem Let us start by formally defining the SCS problem in its decisional version: Shortest Common Supersequence Problem Instance: A set L of m strings {s 1 , · · ·  ...  Introduction The Shortest Common Supersequence (SCS) problem is a classical problem from the realm of string analysis.  ... 
doi:10.1007/11494669_7 fatcat:3suohsrbxjdpjetj3bltfnzhxi

Restricted Common Superstring and Restricted Common Supersequence [article]

Raphaël Clifford, Zvi Gotthilf, Moshe Lewenstein, Alexandru Popa
2010 arXiv   pre-print
The shortest common superstring and the shortest common supersequence are two well studied problems having a wide range of applications.  ...  In this paper we consider both problems with resource constraints, denoted as the Restricted Common Superstring (shortly RCSstr) problem and the Restricted Common Supersequence (shortly RCSseq).  ...  It seems that most of the applications of the shortest common superstring and the shortest common supersequence problem, are more suitable for the case of limited resources.  ... 
arXiv:1004.0424v2 fatcat:uwvvac2ewvho7adgwfcpi66x2i

Memetic Algorithms with Partial Lamarckism for the Shortest Common Supersequence Problem [chapter]

Carlos Cotta
2005 Lecture Notes in Computer Science  
The Shortest Common Supersequence problem is a hard combinatorial optimization problem with numerous practical applications. We consider the use of memetic algorithms (MAs) for solving this problem.  ...  Introduction The Shortest Common Supersequence Problem (SCSP) is a classical problem from the realm of string analysis.  ...  The Shortest Common Supersequence Problem First of all, let us define the notion of supersequence. Let s and r be two strings of symbols taken from an alphabet Σ.  ... 
doi:10.1007/11499305_9 fatcat:4bjr2cvvmvdjtifm5ikbweseua

An approximate A∗ algorithm and its application to the SCS problem

Gaia Nicosia, Gianpaolo Oriolo
2003 Theoretical Computer Science  
In this paper we deal with algorithm A * and its application to the problem of ÿnding the shortest common supersequence of a set of sequences.  ...  We apply this approach to the solution of the shortest common supersequence problem and show its e ectiveness. (Gianpaolo Oriolo). 0304-3975/02/$ -see front matter c 2002 Elsevier Science B.V.  ...  S is a shortest common supersequence of R, SCS(R), if it is a common supersequence of R with minimal length. For instance, if R ={abdc; bca}, then abdca is a shortest common supersequence.  ... 
doi:10.1016/s0304-3975(02)00085-3 fatcat:dmqgb2lqfze5fgpoqsydtarm64

A Probabilistic Beam Search Approach to the Shortest Common Supersequence Problem [chapter]

Christian Blum, Carlos Cotta, Antonio J. Fernández, José E. Gallardo
2007 Lecture Notes in Computer Science  
The Shortest Common Supersequence Problem (SCSP) is a well-known hard combinatorial optimization problem that formalizes many real world problems.  ...  Introduction The Shortest Common Supersequence Problem (SCSP) is a very well-known problem in the area of string analysis.  ...  The Shortest Common Supersequence Problem First of all, let us introduce some notation that we use in the following.  ... 
doi:10.1007/978-3-540-71615-0_4 fatcat:5y6axijlpjf3flfc6xcqhptoz4

Hardness and Approximation of the Asynchronous Border Minimization Problem [chapter]

Alexandru Popa, Prudence W. H. Wong, Fencol C. C. Yung
2012 Lecture Notes in Computer Science  
The objective of the BMP is to place a set of sequences in the array and to find an embedding of these sequences into a common supersequence such that the sum of the "border length" is minimized.  ...  The Shortest Common Supersequence problem is to find a minimumlength common supersequence.  ...  P-BMP: Finding embedding when placement is given We give a reduction from the Shortest Common Supersequence (SCS) to the P-BMP. Shortest Common Supersequence problem.  ... 
doi:10.1007/978-3-642-29952-0_20 fatcat:akrmp4fo3zhpjnbjdboide7uua

Hardness and Approximation of The Asynchronous Border Minimization Problem [article]

Alexandru Popa and Prudence W.H. Wong and Fencol C.C. Yung
2010 arXiv   pre-print
P-BMP: Finding embedding when placement is given We give a reduction from the Shortest Common Supersequence (SCS) problem to the P-BMP. Shortest Common Supersequence problem.  ...  The shortest common supersequence is D = "0100". The optimal deposition for I(1, 1) is D.  ... 
arXiv:1011.1202v1 fatcat:6qzii7pwirewnk72nho3zi2ixm

Analogs and Duals of the MAST Problem for Sequences and Trees [chapter]

Michael Fellows, Michael Hallett, Chantal Korostensky, Ulrike Stege
1998 Lecture Notes in Computer Science  
Subsequence and Shortest Common Supersequence problems).  ...  The Shortest Common Supersequence problem restricted to inputs consisting of a collection of p-sequences (pSCS) remains NP-complete, as does the analogous Smallest Common Supertree problem restricted to  ...  The Shortest Common Supersequence Problem for p-Sequences We show W 1]-hardness for pSCS parameterized by the number of input sequences.  ... 
doi:10.1007/3-540-68530-8_9 fatcat:e5jhoagourec3i3i2r7qqnhqzi

W-Hardness Under Linear FPT-Reductions: Structural Properties and Further Applications [chapter]

Jianer Chen, Xiuzhen Huang, Iyad A. Kanj, Ge Xia
2005 Lecture Notes in Computer Science  
In consequence, shortest common supersequence is W l [1]-hard.  ...  Theorem 4 . 4 The problems longest common subsequence and shortest common supersequence are W l [1]-hard.  ... 
doi:10.1007/11533719_98 fatcat:ewojc2i2z5gbllf6ynfulngu2a

On the approximation of shortest common supersequences and longest common subsequences [chapter]

Tao Jiang, Ming Li
1994 Lecture Notes in Computer Science  
Given a finite set of sequences S, a shortest common supersequence (SCS) of S is a shortest possible sequence s such that each sequence in S is a subsequence of s.  ...  The problems of finding shortest common supersequences (SCS) and longest common subsequences (LCS) are two well-known NP-hard problems that have applications in many areas, including computational molecular  ...  It is easy to see that S has a common supersequence of length if and only if S' has a common supersequence of length n + t.  ... 
doi:10.1007/3-540-58201-0_68 fatcat:noqkgvgsfzcvbjzcepzugprv3q

Effective Attacks and Provable Defenses for Website Fingerprinting

Tao Wang, Xiang Cai, Rishab Nithyanand, Rob Johnson, Ian Goldberg
2014 USENIX Security Symposium  
We show how simulatable, deterministic defenses can be provably private, and we show that bandwidth overhead optimality can be achieved for these defenses by using a supersequence over anonymity sets of  ...  We present a simple algorithm that approximates a solution to the shortest common supersequence problem.  ...  The shortest D(p 1 ) that satisfies the above condition is in fact the shortest common supersequence, written as f scs (A(p 1 )) = D(p i ) for each 1 ≤ i ≤ E.  ... 
dblp:conf/uss/WangCNJG14 fatcat:bav3v7v54nbyfhl5qy27u62jwa

More on the complexity of common superstring and supersequence problems

Martin Middendorf
1994 Theoretical Computer Science  
., More on the complexity of common superstring and supersequence problems, Theoretical Computer Science 125 (1994) 205-228.  ...  Analogously, the Shortest Common Supersequence (SCSe) problem is the decision version of the problem to find, for a finite set of strings L over an alphabet C and an integer ke N, a string S of length  ...  (ii) Obviously, S is a supersequence of L. From (i) we obtain that a shortest supersequence of L must have length 3r(n2 + 1)/k] -1+ n2 + k for a keN.  ... 
doi:10.1016/0304-3975(92)00074-2 fatcat:dqxnujozujfvlkswrivrmawy2y
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