The Internet Archive has a preservation copy of this work in our general collections.
The file type is `application/pdf`

.

## Filters

##
###
Pancake Flipping with Two Spatulas
[article]

2009
*
arXiv
*
pre-print

In this paper we study several variations

arXiv:0812.3933v2
fatcat:a6fybflzaffr3o6ux2zvr46zpi
*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] . ...##
###
Computing the Diameter of 17-Pancake Graph Using a PC Cluster
[chapter]

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). ...

##
###
Some problems on Cayley graphs

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 ...

##
###
Pancake Flipping with Two Spatulas

2010
*
Electronic Notes in Discrete Mathematics
*

In this paper, we give approximation algorithms for several variations

doi:10.1016/j.endm.2010.05.030
fatcat:qvsmfu46s5an7hj3pxbz2iphoe
*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] . ...##
###
Comparing Star and Pancake Networks
[chapter]

2002
*
Lecture Notes in Computer Science
*

This paper has been contributed in honor

doi:10.1007/3-540-36377-7_2
fatcat:tupsmqy55vfa7acgykos65dfgi
*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. ...##
###
Recursively Divided Pancake Graphs with a Small Network Cost

2021
*
Symmetry
*

A

doi:10.3390/sym13050844
fatcat:eqp6ijczhvfuhp3s4px7jzlerq
*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. ...##
###
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

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*...

##
###
Cycles in the burnt pancake graphs
[article]

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. ...

##
###
Constructing Independent Spanning Trees on Pancake Networks

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 ...

##
###
On the problem of sorting burnt pancakes

1995
*
Discrete Applied Mathematics
*

Equivalently, we seek bounds

doi:10.1016/0166-218x(94)00009-3
fatcat:mlh2udgvnvautmiu444rl6skfi
*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*...##
###
Some relations on prefix reversal generators of the symmetric and hyperoctahedral group
[article]

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. ...

##
###
Pancake Flipping Is Hard
[chapter]

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. ...

##
###
Pancake Flipping is hard

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. ...

##
###
Lower Bounding Edit Distances between Permutations

2013
*
SIAM Journal on Discrete Mathematics
*

These operations often act

doi:10.1137/13090897x
fatcat:ptfrj6zizfdznpuio4igjctbue
*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. ...
« Previous

*Showing results 1 — 15 out of 52 results*