The pancake problem, which has attracted considerable attention [10, 12, 9, 15], concerns the number of prefix reversals or flips needed to sort the elements of an arbitrary permutation. The number of prefix reversals to sort permutations is also the diameter of the often We consider restricted pancake problems, for example when only 3 of the possible n-1 flips are allowed. Let f i denote a fli...

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 ...

An n-pancake graph is a graph whose vertices are the permutations of n symbols and each pair of vertices are connected with an edge if and only if the corresponding permutations can be transitive by a prefix reversal. Since the n-pancake graph has n! vertices, it is known to be a hard problem to compute its diameter by using an algorithm with the polynomial order of the number of vertices. Fund...

In this paper, we give an algorithm for the nodeto-set disjoint paths problem in pancake graphs with its evaluation results. The algorithm is of polynomial order of n for an n-pancake graph. It is based on recursion and divided into two cases according to the distribution of destination nodes in classes into which all the nodes in a pancake graph are categorized. The sum of lengths of paths obt...