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Pancake Flipping with Two Spatulas
[article]
2009
arXiv
pre-print
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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 first study the problem of sorting unsigned permutations by prefix reversals and prefix transpositions and present a 3-approximation algorithm for this problem. ...
The number of flips required to sort the stack of n pancakes is the diameter of the n-dimensional pancake network [4, 5] . ...
arXiv:0812.3933v2
fatcat:a6fybflzaffr3o6ux2zvr46zpi
Computing the Diameter of 17-Pancake Graph Using a PC Cluster
[chapter]
2006
Lecture Notes in Computer Science
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prefix reversal. ...
and 17-pancake graphs by using PC clusters. ...
A part of this research is supported by Japan society for the promotion of sciences, the grant-in-aid(No.16510105). ...
doi:10.1007/11823285_117
fatcat:gdhgbkqxlzf7hpntfdamshh7r4
Some problems on Cayley graphs
2008
Linear Algebra and its Applications
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and molecular biologists such as pancake problem or sorting by reversals, to coding theorists such as the vertex reconstruction problem related to error-correcting codes but not related to Ulam's problem ...
This survey paper presents the historical development of some problems on Cayley graphs which are interesting to graph and group theorists such as Hamiltonicity or diameter problems, to computer scientists ...
Acknowledgments I thank Reza Khosrovshahi for inviting me to participate at the First IPM (Institute for Studies in Theoretical Physics and Mathematics) conference on Algebraic Graph Theory that was held ...
doi:10.1016/j.laa.2008.05.010
fatcat:aw4jerefane77kfhanjxqeivvi
Pancake Flipping with Two Spatulas
2010
Electronic Notes in Discrete Mathematics
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In this paper, we give approximation algorithms for 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 prefix transpositions, prefix transreversals etc. along with the prefix reversals. ...
The number of flips required to sort the stack of n pancakes is the diameter of the n-dimensional pancake network [16, 17] . ...
doi:10.1016/j.endm.2010.05.030
fatcat:qvsmfu46s5an7hj3pxbz2iphoe
Comparing Star and Pancake Networks
[chapter]
2002
Lecture Notes in Computer Science
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This paper has been contributed in honor of Neil Jones' 60th birthday. The second author had the honor of being Neil Jones' first Ph.D. student. ...
We improve this result by taking advantage of a few special features of the embedding. ...
Consider the simulation of the transposition (1 i). Now, the A-blocks representing σi and σi+1 have the same size, so one doesn't know which of these A-blocks to change. ...
doi:10.1007/3-540-36377-7_2
fatcat:tupsmqy55vfa7acgykos65dfgi
Recursively Divided Pancake Graphs with a Small Network Cost
2021
Symmetry
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A pancake sorting problem is modeled using a pancake graph whose classes include burnt pancake graphs, signed permutation graphs, and restricted pancake graphs. The network cost is degree × diameter. ...
Finally, the network cost is compared between the RDP graph and other classes of pancake graphs. ...
Conflicts of Interest: The authors declare no conflicts of interest. ...
doi:10.3390/sym13050844
fatcat:eqp6ijczhvfuhp3s4px7jzlerq
Page 5243 of Mathematical Reviews Vol. , Issue 98H
[page]
1998
Mathematical Reviews
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distinct permutations of length n and a connection between two processors when the label of one is obtained from the other by some prefix reversal. ...
Each permutation is considered as a stack of different size pancakes. The well-known pancake problem concerns the number, f(), of prefix reversals required to sort m pancakes. ...
Vertex reconstruction in Cayley graphs
2009
Discrete Mathematics
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The sets S of generators are specified by applications in coding theory, computer science, molecular biology and physics. ...
The combinatorial properties of Cayley graphs on the symmetric group S n and the signed permutation group B n with respect to this problem are presented. ...
The Cayley graphs on permutations and signed permutations generated by the prefix-reversals of any substring [1, i] , i ≤ n, are known with respect to the open combinatorial pancake problem of sorting ...
doi:10.1016/j.disc.2008.07.039
fatcat:zbneleau4fauhgwgl7pwnicaem
Cycles in the burnt pancake graphs
[article]
2019
arXiv
pre-print
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2018 pre-print arXiv:1808.04890v1 fatcat:ixkjbqzd5rbxbcarsop3fvnir4
The pancake graph P_n is the Cayley graph of the symmetric group S_n on n elements generated by prefix reversals. ...
The burnt pancake graph BP_n, which is the Cayley graph of the group of signed permutations B_n using prefix reversals as generators, has similar properties. ...
Patidar was supported by Indiana University's Global Talent Attraction Program. ...
arXiv:1808.04890v2
fatcat:ujobwmm7orgblnwkpurq4vimci
Constructing Independent Spanning Trees on Pancake Networks
2019
IEEE Access
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The pancake graph is a subclass of Cayley graphs and since Cayley graphs are crucial for designing interconnection networks, constructing ISTs on these graphs is necessary for many practical applications ...
We also present proofs about the construction of ISTs on pancake graph to verify that the correctness of these algorithms. ...
Moreover, the graph's edges are given between permutations transitive by prefix reversals; this means that when two permutations of n elements are generated through prefix reversals, then there exists ...
doi:10.1109/access.2019.2962549
fatcat:6sm6ll7e6fe3nh6ruf5wdrvope
On the problem of sorting burnt pancakes
1995
Discrete Applied Mathematics
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Equivalently, we seek bounds on the number of prefix reversals necessary to sort a list of n elements. Bounds of 17n/16 and (5n + 5)/3 were shown by Gates and Papadimitriou in 1979. ...
Given a stack of n pancakes in arbitrary order, all of different sizes, the goal is to sort them into the size-ordered configuration having the largest pancake on the bottom and the smallest on top. ...
Acknowledgements We would like to thank Mohammad Heydari and Hal Sudborough for helpful discussions and for improving on our results by locating a 48 flip sequence for sorting ...
doi:10.1016/0166-218x(94)00009-3
fatcat:mlh2udgvnvautmiu444rl6skfi
Some relations on prefix reversal generators of the symmetric and hyperoctahedral group
[article]
2018
arXiv
pre-print
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The pancake problem is concerned with sorting a permutation (a stack of pancakes of different diameter) using only prefix reversals (spatula flips). ...
Pancake flips are considered as generators and we study the relations satisfied by them. ...
We also thank Jacob Mooney and Kyle Yohler for independently writing computer code to verify our results. ...
arXiv:1803.01760v2
fatcat:7rkvf6ty3rdr7a3immx2vyu4hu
Pancake Flipping Is Hard
[chapter]
2012
Lecture Notes in Computer Science
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pancakes above it (that is, to perform a prefix reversal). ...
Pancake Flipping is the problem of sorting a stack of pancakes of different sizes (that is, a permutation), when the only allowed operation is to insert a spatula anywhere in the stack and to flip the ...
Stacks of pancakes are represented by permutations, and a flip consists in reversing a prefix of any length. ...
doi:10.1007/978-3-642-32589-2_24
fatcat:wp2lw37yeraidjpcxlicncmvem
Pancake Flipping is hard
2015
Journal of computer and system sciences (Print)
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pancakes above it (that is, to perform a prefix reversal). ...
Pancake Flipping is the problem of sorting a stack of pancakes of different sizes (that is, a permutation), when the only allowed operation is to insert a spatula anywhere in the stack and to flip the ...
Stacks of pancakes are represented by permutations, and a flip consists in reversing a prefix of any length. ...
doi:10.1016/j.jcss.2015.02.003
fatcat:aswi253fi5bebkqylewwgspxri
Lower Bounding Edit Distances between Permutations
2013
SIAM Journal on Discrete Mathematics
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These operations often act on just one or two segments of the permutation, e.g. by reversing one segment or exchanging two segments. ...
Moreover, we use our approach to improve the best known lower bound on the prefix transposition diameter from 2n/3 to 3n/4, and investigate a few relations between some statistics on π and π̅. ...
[14] allowed the extension of Tables 1 and 2 by two lines. ...
doi:10.1137/13090897x
fatcat:ptfrj6zizfdznpuio4igjctbue
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