Some new matroids on graphs: cut sets and the max cut problem
Mathematics of Operations Research
A graph theoretic approach to statistical data security
SIAM Journal on Computing
Magic graphs, a characterization
European Journal of Combinatorics
Efficient detection and protection of information in cross tabulated tables I: linear invariant test
SIAM Journal on Discrete Mathematics
A universal-scheme approach to statistical databases containing homogeneous summary tables
ACM Transactions on Database Systems (TODS)
Data Security Equals Graph Connectivity
SIAM Journal on Discrete Mathematics
Total Protection of Analytic-Invariant Information in Cross-Tabulated Tables
SIAM Journal on Computing
A Linear Algorithm for Finding the Invariant Edges of an Edge-Weighted Graph
SIAM Journal on Computing
On the Data Model and Access Method of Summary Data Management
IEEE Transactions on Knowledge and Data Engineering
ACSC '95 Proceedings of the 1995 Asian Computing Science Conference on Algorithms, Concurrency and Knowledge
A Model of Summary Data and its Applications in Statistical Databases
Proceedings of the 4th International Working Conference SSDBM on Statistical and Scientific Database Management
Computational Issues Connected with the Protection of Sensitive Statistics by Auditing Sum Queries
SSDBM '98 Proceedings of the 10th International Conference on Scientific and Statistical Database Management
Answering queries using views: A survey
The VLDB Journal — The International Journal on Very Large Data Bases
On the content of materialized aggregate views
Journal of Computer and System Sciences - Special issue on PODS 2000
Graph Theory With Applications
Graph Theory With Applications
Auditing sum-queries to make a statistical database secure
ACM Transactions on Information and System Security (TISSEC)
An analytical approach to the inference of summary data of additive type
Theoretical Computer Science
Hi-index | 5.23 |
A weighting of vertices of a graph is admissible if there exists an edge weighting such that the weight of each vertex equals the sum of weights of its incident edges. Given an admissible vertex weighting of a graph, an invariant set is an edge set such that the sum of the weights of its edges is the same for every edge weighting, and a nonempty invariant set is minimal if none of its nonempty proper subsets is an invariant set. It is easily seen that every nonempty invariant set is a disjoint union of minimal invariant sets. A graphical characterisation of minimal invariant sets in a bipartite graph is known both in the case the vertex weights are reals and in the case the vertex weights are nonnegative reals. We shall state a graphical characterisation of minimal invariant sets in an arbitrary vertex-weighted graph. Moreover, we give a linear algorithm to test an invariant set for minimality. Finally, we state a complete axiomatisation of invariant sets and give a polynomial algorithm to find a set of minimal invariant sets that completely characterise the set of all invariant sets.