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Coordinating Pebble Motion On Graphs, The Diameter Of Permutation Groups, And Applications

1984
*
25th Annual Symposium onFoundations of Computer Science, 1984.
*

We nlbo consider the rlucsf ion

doi:10.1109/sfcs.1984.715921
dblp:conf/focs/KornhauserMS84
fatcat:qjqi77rq6bcsfhbfmx4nweezjq
*of**permutation*group*diameter*. Driscoli and I h r s t (1983) ohtairic4 a polynoinial upper bound*on*thc*diameter**of*groups grnrrnt,rd by bounded lrrigth cyclrs. ... ,ounds*on*the numbei*of*Inovrs required. These resalts extend thosc*of*Wilson ;1974), who considered G biconnrctcd and k=n-I, with n o analysis*of*number*of*moves. ... The rest*of*chapter 3 consists*of*a number*of*new results in*permutation*groups, which extend classical theorems by providing upper bounds*on**diameter*. ...##
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Distance and connectivity measures in permutation graphs

2003
*
Discrete Mathematics
*

A

doi:10.1016/s0012-365x(02)00870-1
fatcat:bnjnt5vvrvfa7hh33cimk66fza
*permutation**graph*G π*of*a*graph*G (or generalized prism) is obtained by taking two disjoint copies*of*G and adding an arbitrary matching between the copies. ... In particular we show that if G has no isolates and is not 2K k for k odd, then there exists a*permutation**graph**of*G with edge-connectivity equal to its minimum degree. ... That is, F k is a*permutation**graph**of*the path*on*n = 2 k − 1 vertices, and has*diameter*about 4 log 2 n. 2 By a similar construction it holds that the minimum*diameter**of*the*permutation**graph**of*the ...##
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Some problems on Cayley graphs

2008
*
Linear Algebra and its Applications
*

This survey paper presents the historical development

doi:10.1016/j.laa.2008.05.010
fatcat:aw4jerefane77kfhanjxqeivvi
*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 ...*on*April 21-26, 2007, in Tehran and for his hospitality during my staying in Iran. ...##
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Computing the Diameter of 17-Pancake Graph Using a PC Cluster
[chapter]

2006
*
Lecture Notes in Computer Science
*

An n-pancake

doi:10.1007/11823285_117
fatcat:gdhgbkqxlzf7hpntfdamshh7r4
*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 ... Fundamental approaches*of*the*diameter*computation have been proposed. However, the computation*of*the*diameter**of*15-pancake*graph*has been the limit in practice. ... Tomoyuki Hiroyasu for permission to use the PC cluster*on*Doshisha University. A part*of*this research is supported by Japan society for the promotion*of*sciences, the grant-in-aid(No.16510105). ...##
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Vertex reconstruction in Cayley graphs

2009
*
Discrete Mathematics
*

The combinatorial properties

doi:10.1016/j.disc.2008.07.039
fatcat:zbneleau4fauhgwgl7pwnicaem
*of*Cayley*graphs**on*the symmetric group S n and the signed*permutation*group B n with respect to this problem are presented. ... In this report paper we collect recent results*on*the vertex reconstruction in Cayley*graphs*Cay(G, S). ... Let us note here that*one*more problem which will be discussed below arises*on*Cayley*graphs*. This is the problem*of*establishing the*diameter**of*a Cayley*graph*. ...##
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On The Diameter of Pancake Graphs
[article]

2022
*
arXiv
*
pre-print

The

arXiv:2204.08184v1
fatcat:jiwgkfzj6rcfpelgst6tu7ff5y
*diameter**of*a*graph*is the maximum*of*all distances*on*the*graph*, where the distance between two vertices is the shortest path between them. ... The Pancake*graph*(P_n) represents the group*of*all*permutations**on*n elements, namely S_n, with respect to the generating set containing all prefix reversals. ... bound*on*the value*of*diam(Pn). ...##
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A Comparative Study of Star Graphs and Rotator Graphs

1994
*
1994 International Conference on Parallel Processing-Vol 1 (ICPP'94)
*

Acknowledgements We would like to thank Ramaraghavan Srinivasan for his assistance with the simulation programs and for his comments

doi:10.1109/icpp.1994.18
dblp:conf/icpp/PonnuswamyC94
fatcat:hktb4l5yr5ggpangfpfimo5bri
*on*an earlier version*of*this paper. ... Since these directed Cayley*graphs*have some interesting properties like easy routing, low*diameter*and average*diameter*compared to the star*graph*, a comparative analysis*of*these*graphs*is worthy*of*... The length*of*the container*of*any*graph*is the upper bound for the fault*diameter**of*the*graph*9, 10]. ...##
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A 1.375-Approximation Algorithm for Sorting by Transpositions

2006
*
IEEE/ACM Transactions on Computational Biology & Bioinformatics
*

The algorithm is based

doi:10.1109/tcbb.2006.44
pmid:17085846
fatcat:riw53h4j6zeonhcivqhca6j6qu
*on*a new upper bound*on*the*diameter**of*3-*permutations*. ...*of*2-*permutations*and simple*permutations*. ... We prove an upper bound*of*11 n 24 + 3 (n/3 mod 8) 2 + 1*on*the*diameter**of*3-*permutations*. ...##
###
A 1.375-Approximation Algorithm for Sorting by Transpositions
[chapter]

2005
*
Lecture Notes in Computer Science
*

The algorithm is based

doi:10.1007/11557067_17
fatcat:thxu6wgs2fdkta33wczo5y4pmq
*on*a new upper bound*on*the*diameter**of*3-*permutations*. ...*of*2-*permutations*and simple*permutations*. ... We prove an upper bound*of*11 n 24 + 3 (n/3 mod 8) 2 + 1*on*the*diameter**of*3-*permutations*. ...##
###
Oriented Diameter of Star Graphs
[article]

2019
*
arXiv
*
pre-print

The n-star

arXiv:1911.10340v1
fatcat:xq6gmpjfbnazlfwvcy43jzcyoa
*graph*S_n consists*of*n! vertices, each labelled with a distinct*permutation**of*[n]. Two vertices are adjacent if their labels differ exactly in the first and*one*other position. ... An orientation*of*an undirected*graph*G is an assignment*of*exactly*one*direction to each edge*of*G. ... [9] continues the algorithmic study*on*oriented*diameter**on*chordal*graphs*. They show that every chordal*graph*G has an oriented*diameter*at most 2 diam(G) + 1. ...##
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On the diameter of Eulerian orientations of graphs

2006
*
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
*

The result also shows that the directed and undirected versions

doi:10.1145/1109557.1109648
fatcat:gna44cf5tbabnp7rlxt44dcg3e
*of*long standing conjectures regarding the*diameter**of*Cayley*graphs**of*various classes*of*groups, including transitive*permutation*groups ... It follows that recent polynomial bounds*on*the*diameter**of*certain large classes*of*Cayley*graphs**of*the symmetric group and certain linear groups automatically extend to directed Cayley*graphs*. ... Distance in and*diameter**of*Cayley*graphs**of**permutation*groups are computationally hard parameters. ...##
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Processor interconnection networks from Cayley graphs

1992
*
Discrete Applied Mathematics
*

The importance

doi:10.1016/0166-218x(92)90005-u
fatcat:xe5xavk6jbhg5hw77hrcst7czq
*of*the average*diameter*in determining network performance was supported by the fact that the*graphs*found by us had the smallest average*diameter*and outperformed all other*graphs*evaluated ... to produce a fast efficient routing algorithm*on*the associated Cayley*graph*. ... Robert Morris for his encouragement and assistance through the research phase*of*this work as well as during the preparation*of*this paper. ...##
###
Diameter of the commutation classes graph of a permutation
[article]

2022
*
arXiv
*
pre-print

We define a statistic

arXiv:2202.07313v1
fatcat:y43pruvpq5fwtbqnsjimtnu2zq
*on*the*graph**of*commutation classes*of*a*permutation**of*the symmetric group which is used to show that these*graphs*are equipped with a ranked poset structure, with a minimum and ... This characterization also allows us to compute the*diameter**of*the commutation*graph*for any*permutation*, from which the results for the longest*permutation*and for fully commutative*permutations*are ...*one*)*of*the*permutation*in the line above. ...##
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Computing short generator sequences

1987
*
Information and Computation
*

The Cayley

doi:10.1016/0890-5401(87)90043-5
fatcat:myrqklx3unbt3l4oh3c6akqnqm
*graph*is the*graph*whose vertices are the elements*of*G, with edges between vertices p and q iff pg, = q, for some generator gj. The*diameter**of*a group is very dependent*on*presentation. ... Another way to say the same thing is to say that diam(G) is the*graph*-theoretic*diameter**of*the Cayley*graph*f(G). ...##
###
Bounds for the diameters of orbital graphs of affine groups
[article]

2022
*
arXiv
*
pre-print

General bounds are presented for the

arXiv:2205.03593v1
fatcat:zh65tgqt3rdjxguxumbyqojljm
*diameters**of*orbital*graphs**of*finite affine primitive*permutation*groups. ... Several infinite families*of*affine primitive*permutation*groups with large orbital*diameter*are constructed. The results are independent from the classification*of*finite simple groups. ... Acknowledgement The authors would like to thank Sean Eberhard and László Pyber for comments*on*an earlier version*of*the paper. ...
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