Download Algorithms and Discrete Applied Mathematics: Second by Sathish Govindarajan, Anil Maheshwari PDF

By Sathish Govindarajan, Anil Maheshwari

This publication collects the refereed lawsuits of the second one overseas convention on Algorithms and Discrete utilized arithmetic, CALDAM 2016, held in Thiruvananthapuram, India, in February 2016. the quantity comprises 30 complete revised papers from ninety submissions besides 1 invited speak awarded on the convention. The convention specializes in subject matters on the topic of effective algorithms and information buildings, their research (both theoretical and experimental) and the mathematical difficulties bobbing up thereof, and new functions of discrete arithmetic, advances in present functions and improvement of recent instruments for discrete mathematics.

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Extra resources for Algorithms and Discrete Applied Mathematics: Second International Conference, CALDAM 2016, Thiruvananthapuram, India, February 18-20, 2016, Proceedings

Example text

Let us take L = d(u0 , ui ) = i=1 n 10. , v2m , u2m ). So d(u0 , u2m ) = m + 2. , v2p+1 , u2p+1 ). So d(u0 , u2p+1 ) = p + 3. According to different values of n, the range of 2m and 2p + 1 are given as below. For n ≡ 0, 1, 2, or 3 (mod 4) the range of 2m and 2p + 1 are respectively 4 < 2m ≤ n2 and 4 < 2p + 1 ≤ n2 − 1; 4 < 2m ≤ n2 and 4 < 2p + 1 < n2 ; 4 < 2m ≤ n2 − 1 and 4 < 2p + 1 ≤ n2 ; or 4 < 2m < n2 and 4 < 2p + 1 ≤ n2 . n−1 Nowk11 = d(u0 , ui ) i=0 ⎧n 2 −1 ⎪ ⎪ ⎪ [d(u0 , ui ) + d(u0 , un−i )] + d(u0 , u n2 ), n ≡ 0 or 2 (mod 4), ⎪ ⎪ ⎪ ⎪ i=1 ⎨ = ⎪ ⎪ ⎪ n ⎪ 2 ⎪ ⎪ ⎪ [d(u0 , ui ) + d(u0 , un−i )], n ≡ 1 or 3 (mod 4).

R. Soc. Lond. Philos. Trans. B 349, 241–247 (1995) 15. : Comparison of five methods for finding conserved sequences in multiple alignments of gene regulatory regions. Nucleic Acids Res. 27(19), 3899–3910 (1999) 16. : Algorithms for the maximum subarray problem based on matrix multiplication. In: Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1998, pp. 446–452. Society for Industrial and Applied Mathematics, Philadelphia (1998) 17. : The gene distribution of the human genome.

For each pass of each batch, the k maximum density segments are updated using a linear time selection algorithm [3]. If k > k (U −L), where k is some constant number, a single heap T is constructed for all the passes and all the batches. There will be (U − L + 1) lg(U − L + 1) nodes in the tree. 24 Md. Shafiul Alam and A. Mukhopadhyay Fredrickson’s [6] algorithm is used to search the k maximum density segments from it as before. From Lemmas 4 and 5 we have the following theorem: Theorem 3. The above algorithm solves the k length-constrained maximum density segments problem with uniform length and arbitrary L and U in O(n lg(U − L + 1) + k lg2 (U − L + 2)) time and O((U − L + 1) lg(U − L + 2) + k) working space.

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