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A gene network is modeled as a dynamical random graph whose vertices and edges represent genes and gene-gene interactions, respectively. The network grows through three biological mechanisms: (1) gene duplication and loss; (2) gene-gene interaction adding and removing; and (3) genome duplication. The evolutionary dynamics of gene networks is discussed. It is shown that: (1) the vertex degree distribution...
Recently, several studies taking into account the ability for a gene to be absent or to have some copies in genomes have been proposed, as the examplar distance [6,11] or the gene matching computation between two genomes [3,10]. In this paper, we study the time complexity of the conserved interval distance computation considering duplicated genes using both those two strategies.
In this paper, we present a new model for RNA multiple sequence structural alignment based on the longest common subsequence. We consider both the off-line and on-line cases. For the off-line case, i.e., when the longest common subsequence is given as a linear graph with n vertices, we first present a polynomial O(n2) time algorithm to compute its maximum nested loop. We then consider a...
In computational biology, gene order data is often modelled as signed permutations. A classical problem in genome comparison is to detect conserved segments in a permutation, that is, genes that are co-localised in several species, indicating that they remained grouped during evolution. A second largely studied problem related to gene order data is to compute a minimum scenario of reversals that transforms...
Genomic maps often do not specify the order within some groups of two or more markers. The synthesis of a master map from several sources introduces additional order ambiguity due to markers missing from some sources. We represent each chromosome as a partial order, summarized by a directed acyclic graph (DAG), to account for poor resolution and of missing data. The genome rearrangement problem is...
Phylogenetic reconstruction from gene-rearrangement data is attracting increasing attention from biologists and computer scientists. Methods used in reconstruction include distance-based methods, parsimony methods using sequence encodings, and direct optimization. The latter, pioneered by Sankoff and extended by us with the software suite GRAPPA, is the most accurate approach; however, its exhaustive...
The complexity, approximation and algorithmic issues of several clustering problems are studied. These non-traditional clustering problems arise from recent studies in microarray data analysis. We prove the following results. (1) Two variants of the Order-Preserving Submatrix problem are NP-hard. There are polynomial-time algorithms for the Order-Preserving Submatrix Problem when the condition or...
Horizontal gene transfer (HGT) plays a major role in microbial genome diversification, and is claimed to be rampant among various groups of genes in bacteria. Further, HGT is a major confounding factor for any attempt to reconstruct bacterial phylogenies. As a result, detecting and reconstructing HGT events in groups of organisms has become a major endeavor in biology. The problem of detecting HGT...
A new dynamic programming algorithm with O(n4) time and O(n3) space is presented to predict the RNA secondary structure including nested pseudoknots and a subclass of crossed pseudoknots. Compared with the Jens algorithm of O(n4) time and O(n2) space, this algorithm can predict more complex pseudoknots. Compared with the Rivas algorithm of O(n ...
Using a seed to rapidly “hit” possible homologies for further examination is a common practice to speed up homology search in molecular sequences. It has been shown that a collection of higher weight seeds have better sensitivity than a single lower weight seed at the same speed. However, huge memory requirements diminish the advantages of high weight seeds. This paper describes a two-stage extension...
Given a set of leaf-labelled trees with identical leaf sets, the well-known MAST problem consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. MAST and its variant called MCT are of particular interest in computational biology. This paper presents positive and negative results on the approximation of MAST, MCT and their complement versions,...
In this paper, we study the problem of supporting range sum queries on a compressed sequence of values. For a sequence of nk-bit integers, k ≤ O(log n), our data structures require asymptotically the same amount of storage as the compressed sequence if compressed using the Lempel-Ziv algorithm. The basic structure supports range sum queries in O(log n) time. With an increase by a constant factor in...
We present a new Gray code for combinations that is practical and elegant. We represent combinations as bitstrings with s 0’s and t 1’s, and generate them with a remarkably simple rule: Identify the shortest prefix ending in 010 or 011 (or the entire bitstring if no such prefix exists) and then rotate (shift) it by one position to the right. Since the rotated portion of the string consists of at most...
By considering a new metric, Nikov and Nikova defined the class of error-set correcting codes. These codes differ from the error-correcting codes in the sense that the minimum distance of the code is replaced by a collection of monotone decreasing sets Δ which define the supports of the vectors that do not belong to the code. In this paper we consider a subclass of these codes – so called, ideal codes...
In the well-studied Majority problem, we are given a set of n balls colored with two or more colors, and the goal is to use the minimum number of color comparisons to find a ball of the majority color (i.e., a color that occurs for more than ⌈ n/2 ⌉ times). The Plurality problem has exactly the same setting while the goal is to find a ball of the dominant color (i.e., a color that occurs most often)...
It is known that [3]. The reverse direction of whether ZPPNP is contained in S remains open. We show that if the zero-error algorithm is allowed to ask only one query to the NP oracle (for any input and random string), then it can be simulated in S . That is, we prove that ...
The problems of computing single-valued, analytic branches of the logarithm and square root functions on a bounded, simply connected domain S are studied. If the boundary of S is a polynomial-time computable Jordan curve, the complexity of these problems can be characterized by counting classes # P, MP (or MidBitP), and ⊕ P: The logarithm problem is polynomial-time solvable if and...
A c.e. real x is Solovay reducible to another c.e. real y if x can be approximated at least as efficiently as y by means of increasing computable sequences of rational numbers. The Solovay reducibility classifies elegantly the relative randomness of c.e. reals. Especially, the c.e. random reals are complete unter the Solovay reducibility for c.e. reals. In this paper we investigate an extension of...
The maximum subarray problem for a one- or two-dimensional array is to find the array portion that maiximizes the sum of array elements in it. The K-maximum subarray problem is to find the K subarrays with largest sums. We improve the time complexity for the one-dimensional case from $O(min\{K+n\log^2 n, n\sqrt{K}\})$ for 0 ≤ K ≤ n(n–1)/2 to O(nlog K + K2) for K ≤ n. The latter is...
Many web-based systems have a tiered application architecture, in which a request needs to transverse all the tiers before finishing its processing. One of the most important QoS metrics for these applications is the expected response time for the user. Since the expected response time in any tier depends upon the number of servers allocated to this tier, and a request’s total response time is the...
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