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

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

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

The ninety six revised complete papers provided including abstracts of three invited talks have been rigorously reviewed and chosen from 353 submissions. The papers disguise so much features of theoretical computing device technology and combinatorics concerning 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 place, graph concept, graph algorithms.

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

Sample text

Aj . Let S be a two-dimensional array where S[i, j] is the maximum depth of a nested loop in the sequence ti,j . The values of the array S can be computed as follows. For any 1 ≤ i ≤ n, S[i, i] = 0. Suppose that, for 1 ≤ i < j ≤ n, ai and aj match. Then there is a maximum nested loop of ti,j that contains the edge (ai , aj ). Thus S[i, j] = S[i + 1, j − 1]+ 1. Suppose that ai and aj do not match. Then either ai or aj is not an endpoint of the outermost edge of a maximum nested loop of ti,j .

It is shown in this section that the vertex degree distribution always follows power laws, but the network degree distribution may not (due to genome duplications), instead, it approaches to a power law tail. 1 Vertex Degree Distributions Denote n(t) = |N (t)| and b(t) = |E(t)| the numbers of all vertices and edges of the network at time t, respectively. Suppose that at time t, the i−th vertex vi has xi (t) edges in the network. While joining the new duplicated vertex to other vertices in the network, preferential-attachment principle is applied.

It is not known yet whether this problem is NP-complete. We have the following approximation results. Theorem 2. 5 ) time a loop chain can be computed whose size is at least 12 of the corresponding optimum. Given a set of nested loops we can construct a graph G as follows: each node vi corresponds to a nested loop Li , there is an edge eij between two nodes vi , vj if their corresponding loops Li , Lj overlap. Given two nested loops Li , Lj with depths |Li |, |Lj | respectively, let |Li ∩Lj | be the number of nodes (letters) shared by edges in Li , Lj .

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