Abstract
In thegeneral circular permutation layout problem there are two concentric circles,C in andC out. There are a set ofn inner terminals onC in and a set ofn outer terminals onC out: terminalsi onC in and π i onC out are to be connected by means of a wire, where 1 ≤i ≤n. All wires must be realized in the interior ofC out. Each wire can intersectC in at most once and at mostK wires, for a fixedK, can pass between two adjacent inner terminals. A linear-time algorithm for obtaining a planar homotopy (single-layer realization) of an arbitrary instance of the general circular permutation layout problem, forK ≥ 0, is proposed. Previously,K = 1 has been studied. In this paper the algorithm is also extended to a more general problem, in which the number of wires allowed to pass between each pair of adjacent terminals onC in may be different from pair to pair.
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The work of R. D. Lou and M. Sarrafzadeh was supported in part by the National Science Foundation under Grants MIP-8709074 and MIP-8921540. C. S. Rim, K. Nakajima, and S. Masuda's work was supported in part by the National Science Foundation under Grants MIP-8451510 and CDR-8803012 (Engineering Research Centers Program), and a grant from AT&T.
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Lou, R.D., Sarrafzadeh, M., Rim, C.S. et al. General circular permutation layout. Math. Systems Theory 25, 269–292 (1992). https://doi.org/10.1007/BF01213860
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DOI: https://doi.org/10.1007/BF01213860