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

Cristina Bazgan, Pierre Cazals, Janka Chlebíková
2020 Lecture Notes in Computer Science
Min 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

Jordi Casas-Roma, Jordi Herrera-Joancomartí, Vicenç Torra
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]

Choongbum Lee, Benny Sudakov
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

Choongbum Lee, Benny Sudakov
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

Qing Xing, Ergun Akleman, Jianer Chen, Jonathan L Gross
2010 2010 Shape Modeling International Conference
It has recently been shown that if we twist an arbitrary subset 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]

Jianer Chen
1995 Lecture Notes in Computer Science
k and for 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

Jianer Chen
1997 Theoretical Computer Science
k and for 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

JinGuo Liu, ShuGen Ma, YueChao Wang, Bin Li
2008 Science in China Series F Information Sciences
Each configuration 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

Jay Cummings, Christine A. Kelley
2016 Involve. A Journal of Mathematics
The results in this paper give insight into 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]

Therese Biedl, Goos Kant
1994 Lecture Notes in Computer Science
Doing so we can compute all nal coordinates in linear time. 6 Extensions 6.1 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]

Thomas Thierauf, Fabian Wagner
2008 arXiv   pre-print
As 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

Amos Beimel, Shlomi Dolev
2003 Journal of Cryptology
Our aim is 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]

Tianwei Shen, Siyu Zhu, Tian Fang, Runze Zhang, Long Quan
2016 Lecture Notes in Computer Science
Our approach starts by chaining all but singleton images 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

U. Dogrusoz, M. E. Belviranli, A. Dilek
2013 IEEE Transactions on Visualization and Computer Graphics
We present 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

Jens F. Binder, Sarah L. Buglass, Lucy R. Betts, Jean D. M. Underwood
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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