Abstract
Given a subset R of a set A × B, one may ask whether R contains a subset F which is a bijective function from A onto B. A wet lab algorithm for answering this question is presented. Moreover, when such a bijection is contained in R, the algorithm produces a test tube containing a set of DNA plasmids, each of which encodes such a bijection. The number of steps required by the given procedure grows linearly with the number of ordered pairs in the relation R. All known algorithms for solving this bijection problem on conventional computers require a number of steps that grows exponentially in the number of pairs. Various forms of the Hamiltonian path problem are subsumed by the problem of finding such bijections. The algorithm presented is illustrated by outlining its application to the binary relation determined by the directed graph that occurs in the instance of the directed Hamiltonian path problem with which L. Adleman initiated DNA computing.
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Head, T. (2002). An Aqueous Algorithm for Finding the Bijections Contained in a Binary Relation. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds) Formal and Natural Computing. Lecture Notes in Computer Science, vol 2300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45711-9_19
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DOI: https://doi.org/10.1007/3-540-45711-9_19
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