C. B. Fraser, R. W. Irving, and M. Middendorf, Maximal common subsequences and minimal common supersequences, Information and Computation 124 (1996), no. 2, 145-153. MARTIN MIDDENDORF AND VADIM G. TIMKOVSKY  Home/Search   Document Details and Download   Summary   Related Articles   Check

....= 2 S and m 2 N C(s; u; v; m) L(ww ) where w E u (z E v) is the sequence of symbols that are read by M from the first (second) tape while computing C(s; u; v; m) s I(s) T (s; 0) O(s; 0) T (s; 1) O(s; 1) Figure 3.1: Css machine with 11 states. Proof. By induction on m. If m = 0, then we have C(s; u; v; m) 0 L(ww ) Now let m 0 and let C(s; u; v; m Gamma 1) L(ww ) for all u; v; s. Without loss of generality we can suppose I(s) We have C(s; v; m) 0 L(ww ) While considering C(s; au; v; m) we have the following cases: wa ) O(s; a) 0. ....

....of order i such that every nondominated collation of order i is in H(i) Let h be the generating functions for H(i; m) H(i) C(m) Suppose the h (z) satisfy (z) p(z)q(i) z) 4:4) where p(z) and (z) are functions independent of i and q(i) is a nondecreasing polynomial. If z 0 2 (0; is such that (z 0 ) 1 then Proof. We shall denote jH(i) C(m)j by H(i; m) The set N (i; m) is a subset of the set H(i) C(m) and therefore H(i; 2n) is an upper bound for F (i; n) according to Lemma 4.2. Let Z be the set of all z 2 (0; such that (z) 1. For every y 0 ....

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Robert W. Irving and Campbell B. Fraser. Maximal common subsequences and minimal common supersequences. To appear CPM'94.

....the corresponding generating functions C 0 and C x , x 2 Sigma. Finally C(u; v) X u 0 Eu;v 0 Ev C 0 (u 0 ; v 0 ) These observations yield dynamic programming algorithms for C. Similar methods can be used for the medial strings M and their generating functions M . Irving and Fraser [21] have considered maximal (as opposed to longest) common subsequences and minimal common supersequences. They describe dynamic programming algorithms for finding a shortest maximal common subsequence and a longest minimal common supersequence for a pair of strings. The corresponding problems for ....

R. W. Irving and C. B. Fraser. Maximal common subsequences and minimal common supersequences. To appear in CPM'94.

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C. B. Fraser, R. W. Irving, and M. Middendorf, Maximal common subsequences and minimal common supersequences, Information and Computation 124 (1996), no. 2, 145-153. MARTIN MIDDENDORF AND VADIM G. TIMKOVSKY

.... Later dynamic programming algorithms have been proposed by Timkovsky [T89] Foulser, Li and Yang [FLY92] for nding a shortest common supersequence, by Hsu and Du [HD84] Irving and Fraser [IF92] Hakata and Imai [HI92] for nding a longest common subsequence, and by Irving, Fraser and Middendorf [FIM96] for nding a minimal common supersequence and a maximal common subsequence. Foulser, Li and Yang [FLY92] considered the plan merging problem which is an extension of the shortest common supersequence problem, where the set of given strings is replaced by a plan, i.e. an acyclic directed graph ....

C. B. Fraser, R. W. Irving, and M. Middendorf, Maximal common subsequences and minimal common supersequences, Information and Computation 124 (1996), no. 2, 145-153. MIDDENDORF AND TIMKOVSKY

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R. W. Irving and C. B. Fraser. Maximal common subsequences and minimal common supersequences. In M. Crochemore and D. Gus eld, editors, Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching, number 807 in Lecture Notes in Computer Science, pages 173-183, Asilomar, CA, 1994. Springer-Verlag, Berlin.

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C. B. Fraser and R. W. Irving. Maximal common subsequences and minimal common supersequences. Inf. Comput., 124(2):145-153, 1996.

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