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How to Get a Degree-Anonymous Graph Using Minimum Number of Edge Rotations
[chapter]

2020
*
Lecture Notes in Computer Science
*

Min

doi:10.1007/978-3-030-64843-5_17
fatcat:mi2xgn7ehbduda6imn2bjfgnny
*Anonymous*-*Edge*-*Rotation*asks for*a*given*graph*G and*a*positive integer k*to*find*a**minimum**number**of**edge**rotations*that transform G into*a*k-*degree*-*anonymous**graph*. ... On the positive side, we argue that under some constraints on the*number**of**edges*in*a**graph*and k, Min*Anonymous*-*Edge*-*Rotation*is polynomial-time 2-approximable. ... Conclusion In this paper we initiate the study*of*the complexity*of*Min*Anonymous*-*Edge*-*Rotation*problem in which the task is*to*transform*a*given*graph**to**a*k-*degree**anonymous**graph**using*the*minimum**number*...##
###
Anonymizing graphs: measuring quality for clustering

2014
*
Knowledge and Information Systems
*

*Anonymization*

*of*

*graph*-based data is

*a*problem which has been widely studied last years and several

*anonymization*methods have been developed. ... We want

*to*evaluate whether the generic information loss measures are indicative

*of*the

*usefulness*

*of*the data for subsequent data mining processes. ... We define n = |V |

*to*denote the

*number*

*of*nodes and m = |E|

*to*denote the

*number*

*of*

*edges*. We

*use*G = (V, E) and G = ( V , E)

*to*indicate the original and the

*anonymized*

*graphs*, respectively. ...

##
###
Dirac's theorem for random graphs
[article]

2012
*
arXiv
*
pre-print

*A*classical theorem

*of*Dirac from 1952 asserts that every

*graph*on n vertices with

*minimum*

*degree*at least n/2 is Hamiltonian. In this paper we extend this result

*to*random

*graphs*. ... Motivated by the study

*of*resilience

*of*random

*graph*properties we prove that if p ≫ n /n, then a.a.s. every subgraph

*of*G(n,p) with

*minimum*

*degree*at least (1/2+o(1))np is Hamiltonian. ... We would like

*to*thank Michael Krivelevich for inspiring discussions and conversations. We would also like

*to*thank Alan Frieze and the two

*anonymous*referees for their valuable remarks. ...

##
###
Dirac's theorem for random graphs

2012
*
Random structures & algorithms (Print)
*

*A*classical theorem

*of*Dirac from 1952 asserts that every

*graph*on n vertices with

*minimum*

*degree*at least n/2 is Hamiltonian. In this paper we extend this result

*to*random

*graphs*. ... Motivated by the study

*of*resilience

*of*random

*graph*properties we prove that if p log n/n, then a.a.s. every subgraph

*of*G(n, p) with

*minimum*

*degree*at least (1/2+o(1))np is Hamiltonian. ... We would like

*to*thank Michael Krivelevich for inspiring discussions and conversations. We would also like

*to*thank Alan Frieze and the two

*anonymous*referees for their valuable remarks. ...

##
###
Single-cycle plain-woven objects

2010
*
2010 Shape Modeling International Conference
*

It has recently been shown that if we twist an arbitrary subset

doi:10.1109/smi.2010.13
dblp:conf/smi/XingACG10
fatcat:5p3yu7brmjhsnibnhqzlgb6q6i
*of**edges**of**a*mesh on an orientable surface, the resulting extended*graph**rotation*system (EGRS) can be*used**to*induce*a*cyclic weaving on ... We also demonstrate*how*, starting from*a*mesh,*to*construct*a*large*number**of*single-cycle plain-woven objects. ... Therefore, the*minimum**number**of**edges*that need*to*be twisted in order*to*obtain*a*single-cycle solution is the*number**of**edges*in*a*spanning tree*of*the dual*graph*, i.e. F − 1 = 2E μ − 1. ...##
###
Algorithmic graph embeddings
[chapter]

1995
*
Lecture Notes in Computer Science
*

k and for

doi:10.1007/bfb0030829
fatcat:ajeri7qnl5cnreo3ejohdkbiwq
*a*large class*of**graphs*G ... The complexity*of*embedding*a**graph*into*a*variety*of*topological surfaces is investigated. ... Finally, the author thanks an*anonymous*referee for comments and corrections that have improved the presentation. ...##
###
Algorithmic graph embeddings

1997
*
Theoretical Computer Science
*

k and for

doi:10.1016/s0304-3975(96)00273-3
fatcat:xi342d6vffgifar277c4wv3534
*a*large class*of**graphs*G ... The complexity*of*embedding*a**graph*into*a*variety*of*topological surfaces is investigated. ... Finally, the author thanks an*anonymous*referee for comments and corrections that have improved the presentation. ...##
###
Network-based reconfiguration routes for a self-reconfigurable robot

2008
*
Science in China Series F Information Sciences
*

Each configuration

doi:10.1007/s11432-008-0099-9
fatcat:7j5vjnp3djayffa7ozkqyjbv3a
*of*the robot is defined*to*be*a*node in the weighted and directed configuration network. ... Algorithms in*graph*theory have been*used*in enumerating the available reconfiguration routes and deciding the best reconfiguration route. ... ⎥ ∞ ∞ ∞ ∞ ∞ ⎢ ⎥ ∞ ∞ ∞ ∞ ∞ ⎢ ⎥ ⎢ ⎥ ∞ ∞ ∞ ∞ ∞ ∞ ⎣ ⎦ Reconfiguration planning It is complicated*to**get*the best reconfiguration route when there are*a*large*number**of*configurations and*edges*. ...##
###
On the independence and domination numbers of replacement product graphs

2016
*
Involve. A Journal of Mathematics
*

The results in this paper give insight into

doi:10.2140/involve.2016.9.181
fatcat:yoq4krxo25e3raizb5knk4glaa
*how**to*construct large, sparse*graphs*with optimal independence or domination*numbers*. MSC2010: 05C10. ... The replacement product is*a*noncommutative*graph*operation that has been widely applied in many areas. One*of*its advantages over other*graph*products is its ability*to*produce sparse*graphs*. ... We thank the*anonymous*reviewers for their helpful suggestions that improved the quality*of*this paper. ...##
###
A better heuristic for orthogonal graph drawings
[chapter]

1994
*
Lecture Notes in Computer Science
*

Doing so we can compute all nal coordinates in linear time. 6 Extensions 6.1

doi:10.1007/bfb0049394
fatcat:n4mtnwpfgbfkxhgfei4f4wjz4u
*Graphs*with multiple*edges*If the input-*graph*has*a*vertex v*of**degree*2 then the following heuristic can be*used**to**get*fewer ... In Section 6 we show*how*the algorithm can be*used**to*draw*graphs*with multiple*edges*and*graphs*with higher maximum*degree*. Section 7 contains remarks and open problems. ... We present*a*linear time and space algorithm*to*draw any connected*graph*orthogonally on*a*grid*of*size n n with at most 2n + 2 bends. Each*edge*is bent at most twice. ...##
###
The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace
[article]

2008
*
arXiv
*
pre-print

As

arXiv:0802.2825v1
fatcat:4wecw7whi5bwlpxnknkyood44a
*a*consequence*of*our method we*get*that the isomorphism problem for oriented*graphs*is in NL. We also show that the problems are hard for L. ... The isomorphism problem for planar*graphs*is known*to*be efficiently solvable. ... Acknowledgment We thank Jacobo Torán and the*anonymous*referees for helpful comments on the manuscript. ...##
###
Buses for Anonymous Message Delivery

2003
*
Journal of Cryptology
*

Our aim is

doi:10.1007/s00145-002-0128-6
fatcat:mvi4qzwn3fezrlqwte2et4wcs4
*to*simulate this metaphor in the digital world while keeping the*anonymity**of*the sender and receiver. ...*A*single processor in the network, called*a*mix, serves as*a*relay. Each processor P that wants*to*send*a*message m*to**a*processor Q encrypts m*using*Q's public key*to*obtain m . ... The*number**of*seats in*a*bus equals*to*the*number**of*paths that*use*this link in the bus traveling direction. We next discuss*how**to*reduce the*number**of*buses. ...##
###
Graph-Based Consistent Matching for Structure-from-Motion
[chapter]

2016
*
Lecture Notes in Computer Science
*

Our approach starts by chaining all but singleton images

doi:10.1007/978-3-319-46487-9_9
fatcat:swk4tihytvh43ekfuaw2hpzyne
*using**a*visualsimilarity-based*minimum*spanning tree. ... This paper presents*a**graph*-based image matching method that tackles the issues*of*completeness, efficiency and consistency in*a*unified framework. ... The authors would like*to*thank all the*anonymous*reviewers for their constructive feedbacks. ...##
###
CiSE: A Circular Spring Embedder Layout Algorithm

2013
*
IEEE Transactions on Visualization and Computer Graphics
*

We present

doi:10.1109/tvcg.2012.178
pmid:23559509
fatcat:pd7xfineuzdbbmcauubbink74i
*a*new algorithm for automatic layout*of*clustered*graphs**using**a*circular style. ... Unlike other algorithms generating circular drawings, our algorithm does not require the quotient*graph**to*be acyclic, nor does it sacrifice the*edge*crossing*number**of*individual clusters*to*improve respective ... The authors would also like*to*thank the*anonymous*referees for their extremely helpful comments and suggestions. ...##
###
Online social network data as sociometric markers

2017
*
American Psychologist
*

*Using*

*graph*enumeration techniques, it can be shown that comparatively sparse information on

*a*network is suitable as

*a*sociometric marker that allows for the identification

*of*an individual from the global ... In particular, the general non-

*anonymity*

*of*network data sets is discussed, and an approach is developed

*to*quantify the level

*of*uniqueness that

*a*particular online network bestows upon the individual ... Polya counting can be stated as

*a*colouring problem:

*How*many different ways are there

*to*colour in all

*edges*

*of*

*a*

*graph*? ...

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