k-Metric Antidimension: a Privacy Measure for Social Graphs
Rolando Trujillo-Rasua, Ismael G. Yero

TL;DR
This paper introduces the $k$-metric antidimension as a new graph privacy measure, proposes algorithms to compute it, and analyzes its properties for various graph classes, enhancing social graph privacy evaluation.
Contribution
It defines the $k$-metric antidimension, introduces a new privacy measure $(k, \, ext{ell})$-anonymity, and provides algorithms and theoretical analysis for different graph types.
Findings
Algorithm success rate exceeds 80% for $k$-antiresolving basis.
Algorithm success rate exceeds 90% for $k$-antiresolving set.
Theoretical properties are established for paths, cycles, bipartite graphs, and trees.
Abstract
Let be a simple connected graph and an ordered subset of vertices. The metric representation of a vertex with respect to is the -vector , where represents the length of a shortest path in . The set is called a resolving set for if implies for every . The smallest cardinality of a resolving set is the metric dimension of . In this article we propose, to the best of our knowledge, a new problem in Graph Theory that resembles to the aforementioned metric dimension problem. We call a -antiresolving set if is the largest positive integer such that for every vertex there exist other different vertices with ,…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Graph theory and applications
