Filters








52 Hits in 3.4 sec

Pancake Flipping with Two Spatulas [article]

Masud Hasan, Atif Rahman, M. Sohel Rahman, Mahfuza Sharmin, and Rukhsana Yeasmin
2009 arXiv   pre-print
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]

Shogo Asai, Yuusuke Kounoike, Yuji Shinano, Keiichi Kaneko
2006 Lecture Notes in Computer Science  
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

Elena Konstantinova
2008 Linear Algebra and its Applications  
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

Mahfuza Sharmin, Rukhsana Yeasmin, Masud Hasan, Atif Rahman, M. Sohel Rahman
2010 Electronic Notes in Discrete Mathematics  
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]

Linda Morales, I. Hal Sudborough
2002 Lecture Notes in Computer Science  
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

Jung-Hyun Seo, Hyeong-Ok Lee
2021 Symmetry  
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  
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

Elena Konstantinova
2009 Discrete Mathematics  
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]

Saúl A. Blanco, Charles Buehrle, Akshay Patidar
2019 arXiv   pre-print
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

Dun-Wei Cheng, Chih-Te Chan, Sun-Yuan Hsieh
2019 IEEE Access  
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

David S. Cohen, Manuel Blum
1995 Discrete Applied Mathematics  
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]

Saúl A. Blanco, Charles Buehrle
2018 arXiv   pre-print
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]

Laurent Bulteau, Guillaume Fertin, Irena Rusu
2012 Lecture Notes in Computer Science  
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

Laurent Bulteau, Guillaume Fertin, Irena Rusu
2015 Journal of computer and system sciences (Print)  
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

Anthony Labarre
2013 SIAM Journal on Discrete Mathematics  
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
« Previous Showing results 1 — 15 out of 52 results