arXiv subjects

Ewa J. Infeld

Publications and source records attributed to Ewa J. Infeld.

4 recordsLinked to original sources

arXiv2026

k-Anonymity by Partitions Maximizes Perfect Matchings

The number of perfect matchings in a user-behavior bipartite graph is a natural measure of anonymity: more matchings mean greater uncertainty for an attacker. A fundamental question is which graph structure maximizes this count for a fixed infrastructure cost, represented by the number of edges. We prove that the answer is $k$-anonymity by partitions. Using Brègman's Theorem, we show that partitioning users into equal-sized groups and making each group a complete bipartite component achieves the theoretical upper bound on perfect matchings. For edge counts where an exact partition is impossible, we construct a family of graphs that asymptotically attains this bound as the group size grows. We further prove that this optimality is robust: after an attacker de-anonymizes a user by the most damaging choice, the resulting graph is still a partition graph and remains optimal. Together, these results provide a combinatorial justification for the widespread use of $k$-anonymity by partitions in anonymity system design.

math.CO↗

arXiv2016

Uniform Avoidance Coupling of Simple Random Walks

We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform avoidance coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and that uniform avoidance coupling of simple random walks is impossible on trees, and prove that it is possible on several classes of graphs. We also derive a condition on the vertex neighborhoods in a graph equivalent to that graph admitting a uniform avoidance coupling of simple random walks, and an algorithm that tests this with run time polynomial in the number of vertices.

math.PR↗

arXiv2015

Counting Restricted Dyck Paths Through Random Walks

We show connection between Dyck paths with peaks of bounded height and random walks. The correspondence between a certain class of random walks and such Dyck paths allows us to develop a probabilistic perspective on Chebyshev polynomials.

math.CO↗

arXiv2014

Symmetric Disclosure: a Fresh Look at k-Anonymity

We analyze how the sparsity of a typical aggregate social relation impacts the network overhead of online communication systems designed to provide k-anonymity. Once users are grouped in anonymity sets there will likely be few related pairs of users between any two particular sets, and so the sets need to be large in order to provide cover traffic between them. We can reduce the associated overhead by having both parties in a communication specify both the origin and the target sets of the communication. We propose to call this communication primitive "symmetric disclosure." If in order to retrieve messages a user specifies a group from which he expects to receive them, the negative impact of the sparsity is offset.

cs.CR↗