Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Backtracking (the) Algorithms on the Hamiltonian Cycle Problem   Even though the Hamiltonian cycle problem is NP-complete, many of its problem
instances aren't. In fact, almost all the hard instances reside in one area:
near the Koml\'os-Szemer\'edi bound, of $\frac{1}{2}\ v\cdot ln(v) +
\frac{1}{2}\ v\cdot ln( ln(v))$ edges, where randomly generated graphs have an
approximate 50\% chance of being Hamiltonian. If the number of edges is either
much higher or much lower, the problem is not hard -- most backtracking
algorithms decide such instances in (near) polynomial time. Recently however,
targeted search efforts have identified very hard Hamiltonian cycle problem
instances very far away from the Koml\'os-Szemer\'edi bound. In that study, the
used backtracking algorithm was Vandegriend-Culberson's, which was supposedly
the most efficient of all Hamiltonian backtracking algorithms.
  In this paper, we make a unified large scale quantitative comparison for the
best known backtracking algorithms described between 1877 and 2016. We confirm
the suspicion that the Koml\'os-Szemer\'edi bound is a hard area for all
backtracking algorithms, but also that Vandegriend-Culberson is indeed the most
efficient algorithm, when expressed in consumed computing time. When measured
in recursive effectiveness however, the algorithm by Frank Rubin, almost half a
century old, performs best. In a more general algorithmic assessment, we
conjecture that edge pruning and non-Hamiltonicity checks might be largely
responsible for these recursive savings. When expressed in system time however,
denser problem instances require much more time per recursion. This is most
likely due to the costliness of the extra search pruning procedures, which are
relatively elaborate. We supply large amounts of experimental data, and a
unified single-program implementation for all six algorithms. All data and
algorithmic source code is made public for further use by our colleagues.

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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas