Unformatted text preview: ertex exactly once. The Hamiltonian Path Problem is to decide for any given graph with speciﬁed start and end vertices whether a Hamiltonian path exists or not. The Hamiltonian Path Problem has been extensively studied by computer scientists. No efﬁcient (that is, fast) algorithm to solve it has ever emerged. In fact, it seems likely that even using the best currently available algorithms and computers, there are some graphs of fewer than 100 vertices for which determining whether a Hamiltonian path exists would require hundreds of years. In the early 1970s the Hamiltonian Path Problem was shown to be “NPcomplete.” Without going into the theory of NP-completeness, sufﬁce it to say that this ﬁnding convinced most theoretical computer scientists that no efﬁcient algorithm for the problem is possible at all (though proving this remains the most important open problem in theoretical computer science, the so-called NP = P? problem [see “Turing Machines,” by John E. Hopcroft; Scientiﬁc American, May...
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- Fall '08
- DNA, Hamiltonian path, DNA computer