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- W2076475223 abstract "Given a Cartesian productG=G1× ? ×Gm(m? 2) of nontrivial connected graphsGiand then-dimensional baseBde Bruijn graphD=DB(n), it is investigated whether or notGis a spanning subgraph ofD. Special attention is given to graphsG1× ? ×Gmwhich are relevant for parallel computing, namely, to Cartesian products of paths (grids) or cycles (tori). For 2-dimensional de Bruijn graphsD, we present a theorem stating that certain structural assumptions on the factorsG1, ?,Gmensure thatG1× ? ×Gmis a spanning subgraph ofD. As corollaries, we obtain results improving previous results of Heydemannet al.(J. Parallel Distrib. Comput.23 (1994), 104?111) on embedding grids and tori into de Bruijn graphs. Specifically, we obtain that (i) any gridG=G1× ? ×Gmis a spanning subgraph ofD=DB(2) provided that |G| = |D|, and (ii) any torusG=G1× ? ×Gmis a spanning subgraph ofD=DB(2) provided that |G| = |D| and that theGiare cycles of even length ?4. We show that these results have consequences for the casen> 2, too: for evenn, we apply our results to obtain embeddings of grids and toriGinto de Bruijn graphsDB(n) with dilationn/2, where the baseBis a fixed integer ?2, andnis big enough to ensure |G| ? |DB(n)|. We also contrast our results forn= 2 with nonexistence results forn? 3 and briefly describe experimental results in the area of parallel image processing." @default.
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- W2076475223 date "1997-11-01" @default.
- W2076475223 modified "2023-09-24" @default.
- W2076475223 title "Embedding Cartesian Products of Graphs into de Bruijn Graphs" @default.
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- W2076475223 doi "https://doi.org/10.1006/jpdc.1997.1384" @default.
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