On the Diameter of the Pancake Network

Heydari, Mahdi; Sudborough, Ivan Hal

doi:10.1006/jagm.1997.0874

Cited by 102 publications

(60 citation statements)

References 3 publications

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“…The pancake flipping problem [1][2][3][4][5] deals with finding the minimum number of prefix reversals (i.e., flips) required to sort a given permutation. This problem was first introduced in 1975 by [1] which describes the motivation of a chef to rearrange a stack of pancakes from the smallest pancake on the top to the largest one on the bottom by grabbing several pancakes from the top with his spatula and flipping them over, repeating them as many times as necessary.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The number of flips required to sort the stack of n pancakes is the diameter of the n-dimensional pancake network [4,5]. The diameter of a network is the maximum distance between any pair of nodes in the network and corresponds to the worst communication delay for broadcasting messages in the network [4,5]. A well studied variation of pancake flipping problem is the burnt pancake flipping problem [2,4,5] where each element in the permutation has a sign, and the sign of an element changes with reversals.…”

Section: Introductionmentioning

confidence: 99%

“…The diameter of a network is the maximum distance between any pair of nodes in the network and corresponds to the worst communication delay for broadcasting messages in the network [4,5]. A well studied variation of pancake flipping problem is the burnt pancake flipping problem [2,4,5] where each element in the permutation has a sign, and the sign of an element changes with reversals. Pancake and burnt pancake networks have better diameter and better vertex degree than the popular hypercubes [4].…”

Section: Introductionmentioning

confidence: 99%

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Pancake Flipping with Two Spatulas

Sharmin

Yeasmin

Hasan

et al. 2010

Electronic Notes in Discrete Mathematics

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Abstract. In this paper we study several variations of the pancake flipping problem, which is also well known as the problem of sorting by prefix reversals. We consider the variations in the sorting process by adding with prefix reversals other similar operations such as prefix transpositions and prefix transreversals. These type of sorting problems have applications in interconnection networks and computational biology. We first study the problem of sorting unsigned permutations by prefix reversals and prefix transpositions and present a 3-approximation algorithm for this problem. Then we give a 2-approximation algorithm for sorting by prefix reversals and prefix transreversals. We also provide a 3-approximation algorithm for sorting by prefix reversals and prefix transpositions where the operations are always applied at the unsorted suffix of the permutation. We further analyze the problem in more practical way and show quantitatively how approximation ratios of our algorithms improve with the increase of number of prefix reversals applied by optimal algorithms. Finally, we present experimental results to support our analysis.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pancake Flipping with Two Spatulas

Sharmin

Yeasmin

Hasan

et al. 2010

Electronic Notes in Discrete Mathematics

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“…The problem is still open. Some upper and lower bounds [5,6] as well as exact values for 2 n 19 [1,2] are known. One of the main difficulties in solving this problem is the complicated cycle structure of the Pancake graph.…”

Section: Introductionmentioning

confidence: 99%

Small cycles in the Pancake graph

Konstantinova

Medvedev

2013

Ars Math. Contemp.

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The Pancake graph is well known because of the open Pancake problem. It has the structure that any l-cycle, 6 l n!, can be embedded in the Pancake graph P n , n 3. Recently it was shown that there are exactly n! 6 independent 6-cycles and n!(n − 3) distinct 7-cycles in the graph. In this paper we characterize all distinct 8-cycles by giving their canonical forms as products of generating elements. It is shown that there are exactly n!(n 3 +12n 2 −103n+176) 16 distinct 8-cycles in P n , n 4. A maximal set of independent 8-cycles contains n! 8 of these.

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Advances in Genome Rearrangement Algorithms

Hasan

Rahman²

2010

Algorithms in Computational Molecular Biology

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On the Diameter of the Pancake Network

Cited by 102 publications

References 3 publications

Pancake Flipping with Two Spatulas

Pancake Flipping with Two Spatulas

Small cycles in the Pancake graph

Advances in Genome Rearrangement Algorithms

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