Computing and Combinatorics: 11th Annual International by Leslie G. Valiant (auth.), Lusheng Wang (eds.)

By Leslie G. Valiant (auth.), Lusheng Wang (eds.)

The refereed lawsuits of the eleventh Annual foreign Computing and Combinatorics convention, COCOON 2005, held in Kunming, China in August 2005.

The ninety six revised complete papers awarded including abstracts of three invited talks have been rigorously reviewed and chosen from 353 submissions. The papers hide so much facets of theoretical machine technological know-how and combinatorics with regards to computing and are geared up in topical sections on bioinformatics, networks, string algorithms, scheduling, complexity, steiner bushes, graph drawing and format layout, quantum computing, randomized algorithms, geometry, codes, finance, facility situation, graph thought, graph algorithms.

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Additional info for Computing and Combinatorics: 11th Annual International Conference, COCOON 2005, Kunming, China, August 16-29, 2005. Proceedings

Sample text

However, it is still not completely known how such a ncRNA folds into secondary and tertiary structures. One of the method is to take a multiple sequence of ncRNAs and investigate their common folding patterns or secondary structures [4, 19, 20]. In [4], it is proposed that the largest common nested linear subgraph of m given linear graphs (induced by m ncRNA sequences of length n) presents a solution for this problem. This problem is NP-complete and the authors presented an O(log2 n) approximation for this problem [4].

The first problem is based on the idea that the (maximum) deepest nested loop is likely to occur in ncRNA folding (Figure 1 (1)). The second problem is based on the idea that a chain of loops is likely to fold compactly with some specified regions (Figure 1 (2)). an , ai ∈ {A, C, G, U }, and the corresponding linear graph G(t), compute the maximum or the deepest nested loop (MNL) in G(t). We have the following theorem. Theorem 1. an , ai ∈ {A, C, G, U }, and the corresponding linear graph G(t), the maximum nested loop can be computed in O(n2 ) time.

In other words, genes 3 and −3 are of the same family. Let us detail the construction of the two genomes G and H. Let y = |E| + 2 if |E| is even, y = |E| + 1 otherwise. (i − 1) for any 1 ≤ i ≤ m + 1. From (C, E), we construct two genomes G and H as described below (an illustration is given in Figure 1): G1 = γ|E|+1 γ|E|+2 . . γ|E|+m−1 α1 β1 . . αm βm γ1 γ|E|+m γ2 γ|E|+m+1 . . γ2|E|+m−1 γ|E| H1 = α1 θ1 γ|E|+1 α2 θ2 γ|E|+2 . . γ|E|+m−1 αm θm γ|E|+m γ|E|+m+1 . . γ2|E|+m−1 We now detail the substrings that compose G1 and H1 : – for 1 ≤ i ≤ m, we construct the sequences of genes αi = zi and βi = zi +1 zi +2 .

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