Abstract
Combinatorial algorithms that list combinatorial objects in minimal change order are of fundamental interest in computer science and mathematics. In minimal change ordering, successive elements differ in some pre-specified small way. In this paper, we deal with the generation of paths in a special type of minimal change ordering, the revolving door ordering. We propose a simple algorithm to list all paths in a complete graph, K n , with n vertices in revolving door order such that each path is generated exactly once. The algorithm is built using space and time efficient schemes that list all spanning paths and “path sets” in revolving door order. Our algorithm is optimal in the sense that it operates in constant amortized time (CAT) and uses linear space.
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References
Nijenhuis, A., Wilf, H.S.: Combinatorial Algorithms for Computers and Calculators. Academic Press, London (1978)
Trotter, F.H.: Perm (algorithm 115). Communications of the ACM 8, 434–435 (1962)
Ruskey, F., Williams, A.: Generating combinations by prefix shifts. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 570–576. Springer, Heidelberg (2005)
Harada, K.: Generation of rosary permutations expressed in hamiltonian circuits. Communications of the ACM 14, 373–379 (1971)
Knuth, D.E.: Art of Computer Programming, vol. 4. Addison-Wesley, Reading (2005)
Korsh, J., Lafollette, P.: A loopless gray code for rooted trees. ACM Trans. Algorithms 2(2), 135–152 (2006)
Langdon, G.G.: An algorithm for generating permutations. Communications of the ACM 10, 298–299 (1967)
Savage, C.: A survey of combinatorial Gray codes. SIAM Review 39(4), 605–629 (1997)
Johnson, S.M.: Generation of permutations by adjacent transposition. Math. Comp. 17, 282–285 (1963)
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Alamgir, Z., Abbasi, S. (2007). Combinatorial Algorithms for Listing Paths in Minimal Change Order. In: Janssen, J., Prałat, P. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2007. Lecture Notes in Computer Science, vol 4852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77294-1_11
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DOI: https://doi.org/10.1007/978-3-540-77294-1_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77293-4
Online ISBN: 978-3-540-77294-1
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