On selecting a satisfying truth assignment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Randomized algorithms
Approximating the Longest Cycle Problem in Sparse Graphs
SIAM Journal on Computing
Finding a Path of Superlogarithmic Length
SIAM Journal on Computing
A random graph approach to NMR sequential assignment
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Finding paths and cycles of superpolylogarithmic length
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Finding large cycles in Hamiltonian graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The np-completeness of the hamiltonian cycle problem in planar diagraphs with degree bound two
Information Processing Letters
Reduced-by-matching Graphs: Toward Simplifying Hamiltonian Circuit Problem
Fundamenta Informaticae
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We analyze the performance of a simple randomized algorithm for finding 2-factors in directed Hamiltonian graphs of out-degree at most two and in undirected Hamiltonian graphs of degree at most three. For the directed case, the algorithm finds a 2-factor in O(n^2) expected time. The analysis of our algorithm is based on random walks on the line and interestingly resembles the analysis of a randomized algorithm for the 2-SAT problem given by Papadimitriou [On selecting a satisfying truth assignment, in: Proc. 32nd Annual IEEE Symp. on the Foundations of Computer Science (FOCS), 1991, p. 163]. For the undirected case, the algorithm finds a 2-factor in O(n^3) expected time. We also analyze random versions of these graphs and show that cycles of length @W(n/logn) can be found with high probability in polynomial time. This partially answers an open question of Broder et al. [Finding hidden Hamilton cycles, Random Structures Algorithms 5 (1994) 395] on finding hidden Hamiltonian cycles in sparse random graphs and improves on a result of Karger et al. [On approximating the longest path in a graph, Algorithmica 18 (1997) 82].