SQUARE45

Let

\mathcal{D}

be a distributed data store managing a dataset

\mathbf{D}

across

N

nodes. Data consistency is maintained by replicating

\mathbf{D}

using a replication factor

R

. To ensure fault tolerance against

f

failures (where

f < R

), a write operation

\text{Write}(\mathbf{d})

must achieve consensus by successfully committing the update to a quorum

W

of nodes, and a read operation

\text{Read}(\mathbf{d})

must query a quorum

R'

of nodes. For strong consistency, the quorums must satisfy the condition:

W + R' > R

This ensures that the intersection of nodes queried for writing and reading is non-empty, guaranteeing that the latest committed version of

\mathbf{d}

is always retrieved.

Distributed Data Management