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Combinatorial Optimization Algorithms

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Handbook of Combinatorial Optimization

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Abstract

Identification of targets, generally virus or bacteria, in a biological sample is a relevant problem in medicine. Biologists can use hybridization experiments to determine whether a specific DNA fragment, that represents the virus, is present in a DNA solution. A probe is a segment of DNA or RNA, labeled with a radioactive isotope, dye, or enzyme, used to find a specific target sequence on a DNA molecule by hybridization. Selecting unique probes through hybridization experiments is a difficult task, especially when targets have a high degree of similarity, for instance, in case of closely related viruses.The nonunique probe selection problem is a challenging problem from a biological and computational point of view; a plethora of methods have been proposed in literature ranging from evolutionary algorithms to mathematical programming approaches.In this study, we conducted a survey of the existing computational methods for probe design and selection. We introduced the biological aspects of the problem and examined several issues related to the design and selection of probes: oligonucleotide fingerprinting, maximum distinguishing probe set, minimum cost probe set, and nonunique probe selection.

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Notes

  1. 1.

    For two strings s and t, the Hamming distance H(s, t) is the number of positions where the characters of the two strings differ.

  2. 2.

    Entropy measures the information content of a probe with respect to the set of sequences. Shannon entropy is introduced in [74].

  3. 3.

    We recall that a clique in a graph G = (V, E) is a subset \(C \subseteq V\), such that each pair of vertices in C is connected by an edge.

  4. 4.

    A graph G with n > 1 vertices is said highly connected if the minimum size of a cut, k(G), is > n ∕ 2. A highly connected subgraph is an induced subgraph that is highly connected.

  5. 5.

    Recall that the Hamming distance between two strings of equal length is defined as the number of positions at which the strings differ.

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Authors and Affiliations

  1. Dipartmento di Matematica e Informatica, Universita di Catania, Viale Andrea Doria 6, Catania, Italy

    Elisa Pappalardo

  2. Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Istanbul, Turkey

    Beyza Ahlatcioglu Ozkok

  3. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, 32611, Gainesville, FL, USA

    Panos M. Pardalos

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  1. Elisa Pappalardo
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  2. Beyza Ahlatcioglu Ozkok
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  3. Panos M. Pardalos
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Correspondence to Elisa Pappalardo .

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Editors and Affiliations

  1. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Computer Science, University of Texas, Dallas, Richardson, Texas, USA

    Ding-Zhu Du

  3. Dept. Comp. Sci. & Engineering, University of California, San Diego, La Jolla, California, USA

    Ronald L. Graham

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Pappalardo, E., Ahlatcioglu Ozkok, B., Pardalos, P.M. (2013). Combinatorial Optimization Algorithms. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_67

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