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Serial Computations of Levenshtein Distances
, 1997
"... sequence (LCS) of those strings. If D is the simple Levenshtein distance between two strings having lengths m and n, SES is the length of the shortest edit sequence between the strings, and L is the length of an LCS of the strings, then SES = D and L = (m + n 0D)=2. We will focus on the problem of ..."
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sequence (LCS) of those strings. If D is the simple Levenshtein distance between two strings having lengths m and n, SES is the length of the shortest edit sequence between the strings, and L is the length of an LCS of the strings, then SES = D and L = (m + n 0D)=2. We will focus on the problem of determining the length of an LCS and also on the related problem of recovering an LCS. Another related problem, which will be discussed in Chapter 7, is that of approximate string matching, in which it is desired to locate all positions within string y which begin an approximation to string x containing at most D errors (insertions or deletions). 124 SERIAL COMPUTATIONS OF LEVENSHTEIN DISTANCES procedure CLASSIC( x,<
Transversal Graphs For Partially Ordered Sets: Sequencing, Merging And Scheduling Problems
, 1999
"... . This paper introduces an approach to solving combinatorial optimization problems on partially ordered sets by the reduction to searching sourcesink paths in the related transversal graphs. Dierent techniques are demonstrated in application to nding consistent supersequences, merging partially ..."
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. This paper introduces an approach to solving combinatorial optimization problems on partially ordered sets by the reduction to searching sourcesink paths in the related transversal graphs. Dierent techniques are demonstrated in application to nding consistent supersequences, merging partially ordered sets, and machine scheduling with precedence constraints. Extending the approach to labeled partially ordered sets we also propose a solution for the smallest superplan problem and show its equivalence to the well studied coarsest regular renement problem. For partially ordered sets of a xed width the number of vertices in their transversal graphs is polynomial, so the reduction allows us easily to establish that many related problems are solvable in polynomial or pseudopolynomial time. For example, we establish that the longest consistent supersequence problem with a xed number of given strings can be solved in polynomial time, and that the precedenceconstrained release...
A Specialized Branching and Fathoming Technique for The Longest Common Subsequence Problem
, 2006
"... Abstract⎯Given a set S = {S 1,..., S k} of finite strings, the klongest common subsequence problem (kLCSP) seeks a string L of maximum length such that L is a subsequence of each S i for i = 1,..., k. This paper presents a technique, specialized branching, that solves kLCSP. Specialized branching ..."
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Abstract⎯Given a set S = {S 1,..., S k} of finite strings, the klongest common subsequence problem (kLCSP) seeks a string L of maximum length such that L is a subsequence of each S i for i = 1,..., k. This paper presents a technique, specialized branching, that solves kLCSP. Specialized branching combines the benefits of both dynamic programming and branch and bound to reduce the search space. For large k, this method is shown to be computationally superior to dynamic programming. Keywords⎯Longest common subsequence, Branch and bound, Dynamic programming 1.
Problems Related to Subsequences and Supersequences
, 1999
"... We present an algorithm for building the automaton that searches for all nonoverlapping occurrences of each subsequence from the set of subsequences. Further, we define Directed Acyclic Supersequence Graph and use it to solve the generalized Shortest Common Supersequence problem, the Longest Common ..."
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We present an algorithm for building the automaton that searches for all nonoverlapping occurrences of each subsequence from the set of subsequences. Further, we define Directed Acyclic Supersequence Graph and use it to solve the generalized Shortest Common Supersequence problem, the Longest Common NonSupersequence problem, and the Longest Consistent Supersequence problem.
Discrete Mathematics and Theoretical Computer Science (subm.), by the authors, 26–rev The Master Ring Problem
, 2005
"... We consider the master ring problem (MRP) which often arises in optical network design. Given a network which consists of a collection of interconnected rings R1,..., RK, with n1,..., nK distinct nodes, respectively, we need to find an ordering of the nodes in the network that respects the ordering ..."
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We consider the master ring problem (MRP) which often arises in optical network design. Given a network which consists of a collection of interconnected rings R1,..., RK, with n1,..., nK distinct nodes, respectively, we need to find an ordering of the nodes in the network that respects the ordering of every individual ring, if one exists. Our main result is an exact algorithm for MRP whose running time approaches Q · ∏ K k=1 (nk / √ 2) for some polynomial Q, as the nk values become large. For the ring clearance problem, a special case of practical interest, our algorithm achieves this running time for rings of any size nk ≥ 2. This yields the first nontrivial improvement, by factor of (2 √ 2) K ≈(2.82) K,