Range filters are probabilistic data structures that answer approximate range emptiness queries. They aid in avoiding processing empty range queries and have use cases in many application domains such as key-value stores and social web analytics. However, current range filters do not support dynamically changing and growing datasets. Moreover, several of these designs also exhibit impractically high false positive rates under correlated workloads, which are common in practice. These impediments restrict the applicability of range filters across a wide range of use cases. We introduce Memento filter, the first range filter to simultaneously offer dynamicity, fast operations, and a robust false positive rate for any workload. Memento filter partitions the key universe and clusters its keys according to this partitioning. For each cluster, it stores a fingerprint and a list of key suffixes contiguously. The encoding of these lists makes them amenable to existing dynamic filter structures. Due to the one-to-one mapping from keys to suffixes, Memento filter supports inserts and deletes and can even expand to accommodate a growing dataset. We implement Memento filter on top of a Rank-and-Select Quotient filter and InfiniFilter and demonstrate that it achieves a competitive false positive rate and performance with the state of the art while also providing dynamicity. Due to its dynamicity, Memento filter is the first range filter applicable to B-Trees. We showcase this by integrating Memento filter into WiredTiger, a B-Tree-based key-value store, significantly boosting its performance for mixed workloads.

In this work, we give a unifying view of locality in four settings: distributed algorithms, sequential greedy algorithms, dynamic algorithms, and online algorithms. We introduce a new model of computing, called the online-LOCAL model: the adversary reveals the nodes of the input graph one by one, in the same way as in classical online algorithms, but for each new node we get to see its radius-T neighborhood before choosing the output. We compare the online-LOCAL model with three other models: the LOCAL model of distributed computing, where each node produces its output based on its radius-T neighborhood, its sequential counterpart SLOCAL, and the dynamic-LOCAL model, where changes in the dynamic input graph only influence the radius-T neighborhood of the point of change. The SLOCAL and dynamic-LOCAL models are sandwiched between the LOCAL and online-LOCAL models, with LOCAL being the weakest and online-LOCAL the strongest model. In general, all models are distinct, but we study in particular locally checkable labeling problems (LCLs), which is a family of graph problems studied in the context of distributed graph algorithms. We prove that for LCL problems in paths, cycles, and rooted trees, all models are roughly equivalent: the locality of any LCL problem falls in the same broad class - $O(\log^* n)$, $Θ(\log n)$, or $n^{Θ(1)}$ - in all four models. In particular, this result enables one to generalize prior lower-bound results from the LOCAL model to all four models, and it also allows one to simulate e.g. dynamic-LOCAL algorithms efficiently in the LOCAL model. We also show that this equivalence does not hold in general bipartite graphs. We provide an online-LOCAL algorithm with locality $O(\log n)$ for the $3$-coloring problem in bipartite graphs - this is a problem with locality $Ω(n^{1/2})$ in the LOCAL model and $Ω(n^{1/10})$ in the SLOCAL model.