  Metric Differential Privacy (mDP) extends the concept of Differential Privacy
(DP) to serve as a new paradigm of data perturbation. It is designed to protect
secret data represented in general metric space, such as text data encoded as
word embeddings or geo-location data on the road network or grid maps. To
derive an optimal data perturbation mechanism under mDP, a widely used method
is linear programming (LP), which, however, might suffer from a polynomial
explosion of decision variables, rendering it impractical in large-scale mDP.
  In this paper, our objective is to develop a new computation framework to
enhance the scalability of the LP-based mDP. Considering the connections
established by the mDP constraints among the secret records, we partition the
original secret dataset into various subsets. Building upon the partition, we
reformulate the LP problem for mDP and solve it via Benders Decomposition,
which is composed of two stages: (1) a master program to manage the
perturbation calculation across subsets and (2) a set of subproblems, each
managing the perturbation derivation within a subset. Our experimental results
on multiple datasets, including geo-location data in the road network/grid
maps, text data, and synthetic data, underscore our proposed mechanism's
superior scalability and efficiency.
