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,<

. This paper introduces an approach to solving combinatorial optimization problems on partially ordered sets by the reduction to searching source-sink 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 precedence-constrained release...

Abstract not found

cyclic strings

We present an algorithm for building the automaton that searches for all non-overlapping 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 Non-Supersequence problem, and the Longest Consistent Supersequence problem.