The Phase Transition in Exact Cover
<|reference_start|>The Phase Transition in Exact Cover: We study EC3, a variant of Exact Cover which is equivalent to Positive 1-in-3 SAT. Random instances of EC3 were recently used as benchmarks for simulations of an adiabatic quantum algorithm. Empirical results suggest that EC3 has a phase transition from satisfiability to unsatisfiability when the number of clauses per variable r exceeds some threshold r* ~= 0.62 +- 0.01. Using the method of differential equations, we show that if r <= 0.546 w.h.p. a random instance of EC3 is satisfiable. Combined with previous results this limits the location of the threshold, if it exists, to the range 0.546 < r* < 0.644.<|reference_end|>
@article{kalapala2005the,
    title={The Phase Transition in Exact Cover},
    author={Vamsi Kalapala, Cris Moore},
    journal={arXiv preprint arXiv:cs/0508037},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0508037},
    primaryClass={cs.CC}
}