13 research outputs found
On the Complexity of -Closeness Anonymization and Related Problems
An important issue in releasing individual data is to protect the sensitive
information from being leaked and maliciously utilized. Famous privacy
preserving principles that aim to ensure both data privacy and data integrity,
such as -anonymity and -diversity, have been extensively studied both
theoretically and empirically. Nonetheless, these widely-adopted principles are
still insufficient to prevent attribute disclosure if the attacker has partial
knowledge about the overall sensitive data distribution. The -closeness
principle has been proposed to fix this, which also has the benefit of
supporting numerical sensitive attributes. However, in contrast to
-anonymity and -diversity, the theoretical aspect of -closeness has
not been well investigated.
We initiate the first systematic theoretical study on the -closeness
principle under the commonly-used attribute suppression model. We prove that
for every constant such that , it is NP-hard to find an optimal
-closeness generalization of a given table. The proof consists of several
reductions each of which works for different values of , which together
cover the full range. To complement this negative result, we also provide exact
and fixed-parameter algorithms. Finally, we answer some open questions
regarding the complexity of -anonymity and -diversity left in the
literature.Comment: An extended abstract to appear in DASFAA 201
A survey of parameterized algorithms and the complexity of edge modification
The survey is a comprehensive overview of the developing area of parameterized algorithms for graph modification problems. It describes state of the art in kernelization, subexponential algorithms, and parameterized complexity of graph modification. The main focus is on edge modification problems, where the task is to change some adjacencies in a graph to satisfy some required properties. To facilitate further research, we list many open problems in the area.publishedVersio
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
A Comprehensive Bibliometric Analysis on Social Network Anonymization: Current Approaches and Future Directions
In recent decades, social network anonymization has become a crucial research
field due to its pivotal role in preserving users' privacy. However, the high
diversity of approaches introduced in relevant studies poses a challenge to
gaining a profound understanding of the field. In response to this, the current
study presents an exhaustive and well-structured bibliometric analysis of the
social network anonymization field. To begin our research, related studies from
the period of 2007-2022 were collected from the Scopus Database then
pre-processed. Following this, the VOSviewer was used to visualize the network
of authors' keywords. Subsequently, extensive statistical and network analyses
were performed to identify the most prominent keywords and trending topics.
Additionally, the application of co-word analysis through SciMAT and the
Alluvial diagram allowed us to explore the themes of social network
anonymization and scrutinize their evolution over time. These analyses
culminated in an innovative taxonomy of the existing approaches and
anticipation of potential trends in this domain. To the best of our knowledge,
this is the first bibliometric analysis in the social network anonymization
field, which offers a deeper understanding of the current state and an
insightful roadmap for future research in this domain.Comment: 73 pages, 28 figure
Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable
Graph editing problems have a long history and have been widely studied, with applications in biochemistry and complex network analysis. They generally ask whether an input graph can be modified by inserting and deleting vertices and edges to a graph with the desired property. We consider the problem \textsc{Graph-Edit-to-NDL} (GEN) where the goal is to modify to a graph with a given neighbourhood degree list (NDL). The NDL lists the degrees of the neighbours of vertices in a graph, and is a stronger invariant than the degree sequence, which lists the degrees of vertices.
We show \textsc{Graph-Edit-to-NDL} is NP-complete and study its parameterized complexity. In parameterized complexity, a problem is said to be fixed-parameter tractable with respect to a parameter if it has a solution whose running time is a function that is polynomial in the input size but possibly superpolynomial in the parameter.
Golovach and Mertzios [ICSSR, 2016] studied editing to a graph with a given degree sequence and showed the problem is fixed-parameter tractable when parameterized by , where is the maximum degree of the input graph and is the number of edits. We prove \textsc{Graph-Edit-to-NDL} is fixed-parameter tractable when parameterized by .
Furthermore, we consider a harder problem \textsc{Constrained-Graph-Edit-to-NDL} (CGEN) that imposes constraints on the NDLs of intermediate graphs produced in the sequence. We adapt our FPT algorithm for \textsc{Graph-Edit-to-NDL} to solve \textsc{Constrained-Graph-Edit-to-NDL}, which proves \textsc{Constrained-Graph-Edit-to-NDL} is also fixed-parameter tractable when parameterized by .
Our results imply that, for graph properties that can be expressed as properties of NDLs, editing to a graph with such a property is fixed-parameter tractable when parameterized by . We show that this family of graph properties includes some well-known graph measures used in complex network analysis
Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable
Graph editing problems have a long history and have been widely studied, with applications in biochemistry and complex network analysis. They generally ask whether an input graph can be modified by inserting and deleting vertices and edges to a graph with the desired property. We consider the problem \textsc{Graph-Edit-to-NDL} (GEN) where the goal is to modify to a graph with a given neighbourhood degree list (NDL). The NDL lists the degrees of the neighbours of vertices in a graph, and is a stronger invariant than the degree sequence, which lists the degrees of vertices.
We show \textsc{Graph-Edit-to-NDL} is NP-complete and study its parameterized complexity. In parameterized complexity, a problem is said to be fixed-parameter tractable with respect to a parameter if it has a solution whose running time is a function that is polynomial in the input size but possibly superpolynomial in the parameter.
Golovach and Mertzios [ICSSR, 2016] studied editing to a graph with a given degree sequence and showed the problem is fixed-parameter tractable when parameterized by , where is the maximum degree of the input graph and is the number of edits. We prove \textsc{Graph-Edit-to-NDL} is fixed-parameter tractable when parameterized by .
Furthermore, we consider a harder problem \textsc{Constrained-Graph-Edit-to-NDL} (CGEN) that imposes constraints on the NDLs of intermediate graphs produced in the sequence. We adapt our FPT algorithm for \textsc{Graph-Edit-to-NDL} to solve \textsc{Constrained-Graph-Edit-to-NDL}, which proves \textsc{Constrained-Graph-Edit-to-NDL} is also fixed-parameter tractable when parameterized by .
Our results imply that, for graph properties that can be expressed as properties of NDLs, editing to a graph with such a property is fixed-parameter tractable when parameterized by . We show that this family of graph properties includes some well-known graph measures used in complex network analysis
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum