  Conventional origin-destination (OD) matrices record the count of trips
between pairs of start and end locations, and have been extensively used in
transportation, traffic planning, etc. More recently, due to use case scenarios
such as COVID-19 pandemic spread modeling, it is increasingly important to also
record intermediate points along an individual's path, rather than only the
trip start and end points. This can be achieved by using a multi-dimensional
frequency matrix over a data space partitioning at the desired level of
granularity. However, serious privacy constraints occur when releasing OD
matrix data, and especially when adding multiple intermediate points, which
makes individual trajectories more distinguishable to an attacker. To address
this threat, we propose a technique for privacy-preserving publication of
multi-dimensional OD matrices that achieves differential privacy (DP), the
de-facto standard in private data release. We propose a family of approaches
that factor in important data properties such as data density and homogeneity
in order to build OD matrices that provide provable protection guarantees while
preserving query accuracy. Extensive experiments on real and synthetic datasets
show that the proposed approaches clearly outperform existing state-of-the-art.
