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- W4386870839 abstract "Sawada and Williams in [SODA 2018] and [ACM Trans. Alg. 2020] gave algorithms for constructing Hamiltonian paths and cycles in the Sigma-Tau graph, thereby solving a problem of Nijenhuis and Wilf that had been open for over 40 years. The Sigma-Tau graph is the directed graph whose vertex set consists of all permutations of n, and there is a directed edge from $$pi $$ to $$pi '$$ if $$pi '$$ can be obtained from $$pi $$ either by a cyclic left-shift (sigma) or by exchanging the first two entries (tau). We improve the existing algorithms from $$mathcal{O}(n)$$ time per permutation to $$mathcal{O}(1)$$ time per permutation. Moreover, our algorithms require only $$mathcal{O}(1)$$ extra space. The result is the first combinatorial generation algorithm for n-permutations that is optimal in both time and space, and lists the objects in a Gray code order using only two types of changes. The simple C code ( $$sim $$ 50 lines) can be found at https://github.com/fmasillo/sigma-tau ." @default.
- W4386870839 created "2023-09-20" @default.
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- W4386870839 date "2023-01-01" @default.
- W4386870839 modified "2023-09-27" @default.
- W4386870839 title "Constant Time and Space Updates for the Sigma-Tau Problem" @default.
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- W4386870839 doi "https://doi.org/10.1007/978-3-031-43980-3_26" @default.
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