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In this paper, we describe and illustrate a tool for analyzing and visualizing sequence and distance data, called the splits-graph . The construction of this graph is based upon the split-decomposition technique which is a procedure to decompose a given metric defined on a finite set in a...
With the advent of large-scale DNA physical mapping and sequencing, studies of genome rearrangements are becoming increasingly important in evolutionary molecular biology. From a computational perspective, the study of evolution based on rearrangements leads to a rearrangement distance problem ,...
A fold of a finite string S over a given alphabet is an embedding of S in some fixed infinite grid, such as the square or cubic mesh. The score of a fold is the number of pairs of matching string symbols which are embedded at adjacent grid vertices. Folds of strings in two- and three-dimensional...
We consider the following problem motivated by an application in computational molecular biology. We are given a set of weighted axis-parallel rectangles such that for any pair of rectangles and either axis, the projection of one rectangle does not enclose that of the other. Define a pair to be...
We show how DNA-based computers can be used to solve the satisfiability problem for boolean circuits. Furthermore, we show how DNA computers can solve optimization problems directly without first solving several decision problems. Our methods also enable random sampling of satisfying assignments.
In this paper we address the problem of primer selection in polymerase chain reaction experiments. We prove that the problem of minimizing the number of primers required to amplify a set of DNA sequences is NP -complete. Moreover, we show that it is also intractable to approximate solutions to...
A popular puzzle TOP-SPIN consists of a permutation of 20 numbered disks on an oval track, with a turnstile capable of reversing a string of 4 consecutive disks. The goal is to sort the disks into identity permutation using reversals. We consider the more general case of sorting n element...
The problem of determining whether a given k -colored graph is a subgraph of a properly colored interval graph has an application in DNA physical mapping. In this paper, we study the problem for the case that the number of colors k is fixed. For k = 2, we give a simple linear time algorithm, for...
In the analysis of biological sequences there arises the question of attributing weights to each element of a set of objects in such a way that similar objects do not overly influence deductions based on the entire set of objects. Since there is no known precise statement of this problem, we...
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