Embedding hypercubes into pancake, cycle prefix and substring reversal networks

Among Cayley graphs on the symmetric group, some that have noticeably low diameter relative to the number of generators involved are the pancake network, burnt pancake network, and cycle prefix network [1,6,7,8]. Another such Cayley graph is the star network, and constructions have been given for one-to-one and one-tomany low dilation embeddings of hypercubes into star networks [11,12,15]. For each of dilations 1 through 4, in this paper we construct embeddings of hypercube (and hypercube-like) networks into pancake, burnt pancake, cycle prefix, and substring reversal networks. Embeddings of hypercubes into pancake networks is our focus, the other results being closely related.