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- W2029596898 abstract "The stereo-realization of a graph is the assignment of positions in Cartesian space to each of its vertices such that vertex density is bounded. A bound is derived on the average edge length in such a realization. It is similar to an earlier reported result, however the new bound can be applied to graphs for which the earlier result is not well suited. A more precise realization definition is also presented. The bound is applied to d-dimensional realizations of de Bruijn graphs, yielding an edge length of Ω((1−2−d)rn/d/(2n)), where r is the radix (number of distinct symbols) and n is the number of graph dimensions (number of symbol positions). The bound is also applied to shuffle-exchange graphs; for such graphs with small radix the edge-length bound is , where r is the radix, n is the number of graph dimensions, lσ is the average length of shuffle edges, and le is the average length of exchange edges." @default.
- W2029596898 created "2016-06-24" @default.
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- W2029596898 date "1996-03-01" @default.
- W2029596898 modified "2023-09-26" @default.
- W2029596898 title "A LOWER BOUND ON THE AVERAGE PHYSICAL LENGTH OF EDGES IN THE PHYSICAL REALIZATION OF GRAPHS" @default.
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- W2029596898 doi "https://doi.org/10.1142/s0129626496000145" @default.
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