  Due to the drawbacks of Federated Learning (FL) such as vulnerability of a
single central server, centralized federated learning is shifting to
decentralized federated learning, a paradigm which takes the advantages of
blockchain. A key enabler for adoption of blockchain-based federated learning
is how to select suitable participants to train models collaboratively.
Selecting participants by storing and querying the metadata of data owners on
blockchain could ensure the reliability of selected data owners, which is
helpful to obtain high-quality models in FL. However, querying
multi-dimensional metadata on blockchain needs to traverse every transaction in
each block, making the query time-consuming. An efficient query method for
multi-dimensional metadata in the blockchain for selecting participants in FL
is absent and challenging. In this paper, we propose a novel data structure to
improve the query efficiency within each block named MerkleRB-Tree. In detail,
we leverage Minimal Bounding Rectangle(MBR) and bloom-filters for the query
process of multi-dimensional continuous-valued attributes and discrete-valued
attributes respectively. Furthermore, we migrate the idea of the skip list
along with an MBR and a bloom filter at the head of each block to enhance the
query efficiency for inter-blocks. The performance analysis and extensive
evaluation results on the benchmark dataset demonstrate the superiority of our
method in blockchain-based FL.
