V. Bafna, S. Muthukrishnan, and R. Ravi. Computing similarity between RNA strings. In Z. Galil and E. Ukkonen, editors, Proceedings of the Sixth Annual Symposium on Combinatorial Pattern Matching (CPM-95), Lecture Notes in Computer Science 937, pages 1--16, Berlin, 1995. Springer.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for the so called ordered tree inclusion problem [8] Kilpelainen and Mannila already presented quadratic time algorithms for a strict special case of APS(nested,nested) In their case, sequence information is not taken into account and we can easily derive their problem from ours. Bafna et al. [2], among other things, considered the corresponding arc preserving substring problems. As to LAPCS problems, we only briefly mention that most problems in that context become NP complete [4, 7] as, in particular, LAPCS(nested,nested) That is why researchers focussed on approximation (factor 2) ....

V. Bafna, S. Muthukrishnan, and R. Ravi. Computing similarity between RNA strings. In Proc. of 6th CPM, number 937 in LNCS, pages 1--16, 1995. Springer.

....Markov models (HMMs) capturing well the common primary and secondary structures [16, 4] Notice that the above two methods do not treat basepairs as units of comparison. Instead, they focus on local structures and treat them as subunits. Other work that does not treat base pairs as units includes [5, 2, 12]. On the other hand, there are several papers which consider base pairs as units, and discuss the similarity at a sequence level [17, 28, 27, 6, 8, 10, 14] In this paper, we follow this last line of research and de ne a notion of edit distance between two RNA sequences, taking into consideration ....

.... (or arc altering) operation is much more plausible than rst deleting a base pair and then inserting two single bases (or one single base, respectively) Another line of work related to similarity comparison between RNA secondary and tertiary structures is focussed on primary sequences [2, 5] where the comparison is basically done on the primary sequences while trying to incorporate the secondary and tertiary structural information. The weakness of this approach is that it does not treat a base pair as a whole entity. Our model treats base pairs as basic units and is closer to the ....

V. Bafna, S. Muthukrishnan, and R. Ravi. Computing similarity between RNA strings. In Proceedings of 6th Annual Symposium on Combinatorial Pattern Matching (CPM'95), LNCS 937, pages 1-16, 1995.

....onto the sequence and analyzing the resulting annotated sequence; however, this work has been limited in its use of the annotated information. In particular, arcs between sequence symbols are used in an annotation to represent bonds in RNA secondary structure. Bafna, Muthukrishnan, and Ravi [BMR96] present an algorithm for computing a sequence distance with additional weighting to increase the similarity score when arcs are matched. The algorithm produces an alignment A of strings S 1 and S 2 that maximizes the sum l(A) X 1km 0 fl(S 1 [k Gamma gap[1; k] S 2 [k Gamma gap[2; k] ....

....use that arc, as before. If the penalty w p is higher than all w(x; y) symbol weights, the altered algorithm will still enforce the original prohibition on induced arc mismatch. If w p = 0, then the altered algorithm solves the same subproblem as the O(n 2 m 2 ) algorithm of Bafna et al. [BMR96]. For sequences that are very long and have limited cutwidth (k log 9 n, where n m) the altered algorithm described here will have a worst case time complexity 2 O(n 2 m) So for sequences with limited cutwidth, 127 this algorithm can exploit that limitation to have a smaller time complexity ....

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V. Bafna, S. Muthukrishnan, and R. Ravi. Computing similarity between RNA strings. DIMACS Technical Report 96-30, 1996.

....will be referred to as an arc annotated sequence [6] Observe that a (plain) sequence without any arc annotation can be viewed as an arc annotated sequence with an empty arc set. Arc annotated sequences are useful in describing the secondary and tertiary structures of RNA and protein sequences [1, 4, 6, 8, 10, 12, 14]. For example, one may use arcs to represent bonds between nucleotides in an RNA sequence or contact forces between amino acids in a protein sequence. Therefore, the problem of comparing arc annotated sequences has applications in the structural comparison of RNA and protein sequences and has ....

....bonds between nucleotides in an RNA sequence or contact forces between amino acids in a protein sequence. Therefore, the problem of comparing arc annotated sequences has applications in the structural comparison of RNA and protein sequences and has received much recent attention in the literature [1, 6, 8, 10, 14]. In this paper, we follow the LCS approach proposed in [6] and study the LCS problem for annotated sequences. 1.1 The Arc Annotated LCS Problem and Its Restricted Versions Given two annotated sequences S 1 and S 2 with arc sets P 1 and P 2 respectively, a common subsequence T of S 1 and S 2 ....

V. Bafna, S. Muthukrishnan and R. Ravi, Computing similarity between RNA strings, DIMACS Technical Report 96-30, 1996.

....base pair in RNA secondary structure, but hardly ever certain. We do not consider the probabilistic variant in this paper, but it definitely would be a good topic in our future research. 2 Another referee pointed out that this dynamic programming is similar to a dynamic programming provided in [1, 2]. We have to mention here that although the spirits of the dynamic programming algorithms are similar, the details of computation differ a lot and thus they are capable of different kinds of computing. We also remark that the model in [1, 2] does not require arc preserving, and hence it doesn t ....

....is similar to a dynamic programming provided in [1, 2] We have to mention here that although the spirits of the dynamic programming algorithms are similar, the details of computation differ a lot and thus they are capable of different kinds of computing. We also remark that the model in [1, 2] does not require arc preserving, and hence it doesn t necessarily take a base pair in RNA secondary structures as a unit. The Longest Common Subsequence Problem for Arc Annotated Sequences 11 If i 0 is free, then DP (i; i 0 ; j; j 0 ) max 8 : DP (i; i 0 Gamma 1; j; j 0 Gamma ....

V. Bafna, S. Muthukrishnan, and R. Ravi. Computing similarity between RNA strings. Technical report, DIMACS, 1996. Technical Report 96-30.

....will be referred to as an arc annotated sequence [7] Observe that a (plain) sequence without any arc annotation can be viewed as an arc annotated sequence with an empty arc set. Arc annotated sequences are useful in describing the secondary and tertiary structures of RNA and protein sequences [1, 5, 7, 9, 11, 14, 17]. For example, one may use arcs to represent bonds between nucleotides in an RNA (more precisely, transfer RNA or tRNA) sequence (see Figure 1) or contact forces between amino acids in a protein sequence. Therefore, the problem of comparing arc annotated sequences CAGCGUCACACCCGCGGGGUAAACGCU ....

.... Upsilon Xi ffl fi C A U G C C G G C U A C A C C G C G G C G G C U A A A FIG. 1. A tRNA and its corresponding arc annotated sequence. has applications in the structural comparison of RNA and protein sequences and has received much recent attention in the literature [1, 7, 9, 11, 17]. In this paper, we follow the LCS approach proposed in [7] and study the LCS problem for arc annotated sequences. 1.1 The LAPCS Problem and Its Restricted Versions Given two arc annotated sequences S 1 and S 2 with arc sets P 1 and P 2 respectively, a common subsequence T of S 1 and S 2 induces ....

[Article contains additional citation context not shown here]

V. Bafna, S. Muthukrishnan, and R. Ravi. Computing similarity between RNA strings. In Proceedings of 6th Annual Symposium on Combinatorial Pattern Matching (CPM'95), LNCS 937, pages 1--16, 1995.

....of the problem can often be conveniently modelled through the addition of further constraints to the basic linear program. With dynamic programming, on the other hand, accommodating variations such as considering secondary structure in sequence alignment, as in Bafna, Muthukrishnan and Ravi [3], can cause at a minimum a significant restructuring of the basic recurrences. With the polyhedral approach, much of the code developed for the basic problem can be reused for the problem variations; for example, both the Generalized Maximum Trace and RNA Sequence Alignment problems are based on ....

....) space (n is the length of the sequences) and thus can handle only short sequences. Corpet and Michot propose an anchor point heuristic to divide large alignment problems by fixed alignment regions into small subproblems that the dynamic programming algorithm can then be applied to. Bafna et al. [3] improved the dynamic programming algorithm to a running time of O(n 4 ) which still does not make it applicable to real life problems. Common motifs among several sequences are searched by Waterman [37] Eddy and Durbin [7] describe probabilistic models for measuring the secondary structure and ....

V. Bafna, S. Muthukrishnan, and R. Ravi. Computing similarity between RNA strings. In Z. Galil and E. Ukkonen, editors, Proceedings of the Sixth Annual Symposium on Combinatorial Pattern Matching (CPM-95), Lecture Notes in Computer Science 937, pages 1--16, Berlin, 1995. Springer.

....features, and conversely, no good model of their common structural features may be obtained without a good multiple alignment. Thus the RNA folding and alignment problem looks like the chicken and egg problem. Nevertheless, some methods exist to simultaneously fold and align RNAs (Sankooe 1985; Bafna, Muthukrishnan, Ravi 1995) but they have prohibitive costs in time and, which is worse, in space. In this context, the Covariance Models (CM s) Eddy Durbin 1994) and the more general Stochastic Context Free Grammars (SCFG s) Sakakibara et al. 1994) look very promising because, once constructed for a given family of ....

.... DY6050 extracted from a well known freely available compilation of tRNAs (Steinberg, Misch, Sprinzl 1993) To overcome the high complexities of the previous model, where both RNAs are initially unfolded and unaligned, some authors have tried to align and fold one RNA against already folded RNAs (Bafna, Muthukrishnan, Ravi 1995; Corpet Michot 1994) Once again, MTSAG s are able to successfully capture the subtleties of these methods. In fact, we just have to replace the folded RNA or the family of folded RNAs, against which we are about to align and fold new RNAs, by a special rst tape where paired and unpaired bases ....

Bafna, V.; Muthukrishnan, S.; and Ravi, R. 1995. Computing similarity between RNA strings. In Proceedings of the Sixth Symposium on Combinatorial Pattern Matching, volume 937 of Lecture Notes in Computer Science, 116.

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V. Bafna, S. Muthukrishnan, and R. Ravi. Computing similarity between RNA strings. In Z. Galil and E. Ukkonen, editors, Proceedings of the Sixth Annual Symposium on Combinatorial Pattern Matching (CPM-95), Lecture Notes in Computer Science 937, pages 1--16, Berlin, 1995. Springer.

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