T. M. Y. Wang and C. D. Savage, A Gray code for necklaces of fixed density, SIAM J. Discrete Math., 9 (1996), pp. 654--673.  Home/Search Document Details and Download
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An Efficient Algorithm for Generating Necklaces with Fixed.. - Ruskey, Sawada (1999) (Correct)
....not all necklaces are required, but rather only those of fixed density (the number of zeros is fixed) Previous to this paper, no e#cient generation algorithm for fixed density necklaces was known. Previous fixed density necklace algorithms had running times of O(n N(n, d) Wang and Savage [9]) and O(N(n) Fredricksen and Kessler [4] where N(n, d) denotes the number of necklaces with length n and density d and N(n) denotes the number of necklaces with length n. Wang and Savage base their algorithm on finding a Hamilton cycle in a graph related to a tree of necklaces. The main ....
T. M. Y. Wang and C. D. Savage, A Gray code for necklaces of fixed density, SIAM J. Discrete Math., 9 (1996), pp. 654--673.
A Survey of Combinatorial Gray Codes - Savage (1996) (23 citations) (Correct)
....this is impossible for even n, but for odd n the question remains open. However, in the case of necklaces with a fixed number of 1 s, Wang showed, with a very intricate construction, how to construct a Gray code in which successive necklace representatives differ only by the swap of a 0 and a 1 [Wan94, WS94] (Figure 11. It remains open whether necklaces with a fixed number of 1 s can be generated in constant amortized time, either by a modification the FKM algorithm, by a Gray code, or by any other method. The Gray code adjacency criterion can be generalized to necklaces with k 2 beads by ....
T. M. Y. Wang. A Gray Code for Necklaces of Fixed Density. PhD thesis, Department of Computer Science, North Carolina State University, 1994.
An Efficient Algorithm for Generating Necklaces with Fixed.. - Sawada, Ruskey (Correct)
....no efficient generation algorithm for fixed density necklaces was known. Research supported by NSERC. e mail: jsawada csr.uvic.ca y Research supported by NSERC. e mail: fruskey csr.uvic.ca Previous fixed density necklace algorithms had running times of O(n Delta N(n; d) Wang and Savage [8]) and O(N(n) Fredricksen and Kessler [4] where N(n; d) denotes the number of necklaces with length n and density d and N(n) denotes the number of necklaces with length n. Wang and Savage base their algorithm on finding a Hamilton cycle in a graph related to a tree of necklaces. The main ....
T.M.Y Wang and C.D. Savage, A Gray code for necklaces of fixed density, SIAM J. Discrete Math, 9 (1996) 654-673.
A Survey of Combinatorial Gray Codes - Savage (1996) (23 citations) Self-citation (Savage) (Correct)
....this is impossible for even n, but for odd n the question remains open. However, in the case of necklaces with a fixed number of 1 s, Wang showed, with a very intricate construction, how to construct a Gray code in which successive necklace representatives differ only by the swap of a 0 and a 1 [Wan94, WS94] (Figure 11. It remains open whether necklaces with a fixed number of 1 s can be generated in constant amortized time, either by a modification the FKM algorithm, by a Gray code, or by any other method. The Gray code adjacency criterion can be generalized to necklaces with k 2 beads by ....
T. M. Y. Wang and C. D. Savage. Gray codes for necklaces of fixed density, 1994. Preprint.
A Gray Code for Necklaces of Fixed Density - Wang, Savage (1997) (4 citations) Self-citation (Wang) (Correct)
....of the theorem. At the bottom is the Gray code obtained by replacing each x on C by M [x] 4 The Algorithm The proof of Theorem 2 gives a recursive procedure for constructing a Gray code for necklaces of fixed density. The procedure has been implemented in C and is included in the appendix to [Wan]. A subsequent modification requires storage only O(n) In this section, we show the time required is O(nN(n; d) where N(n; d) is the number of n bit necklaces of density d. Below, we give a crude outline of the procedure CYCLE(x; d; i) for constructing a hamilton cycle in the graph G n [x; ....
T. M. Wang, "Gray codes for necklaces of fixed density," Ph.D. Thesis, Department of Computer Science, North Carolina State University (1994).
An Efficient Algorithm for Generating Necklaces with Fixed.. - Ruskey, Sawada (1999) (Correct)
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T. M. Y. Wang and C. D. Savage, A Gray code for necklaces of fixed density, SIAM J. Discrete Math., 9 (1996), pp. 654--673.
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