DeltaSort: Incremental Sorting of Arrays with Known Updates

When records need to be read in a particular order, sorting at query time incurs repeated Θ(n log n) cost for an array of n records and can become a bottleneck in read-heavy workloads. A common solution is to maintain a derived sorted read-replica that is kept updated as the underlying system-of-record changes. For updating read-replicas that are stored as arrays, existing approaches rely on either full re-sorting or incremental algorithms such as binary insertion or merge-based sort. In this paper, we study incremental sorting under a new model in which the sorting routine is explicitly informed of the k indices updated since the previous sort - a setting that naturally arises in systems that track updates. Under this model, we present DeltaSort, a new algorithm that runs in O(n√k) expected time using O(k) auxiliary space under a random update model, and outperforms existing algorithms for small update batches in our experimental evaluation.