In this paper, we describe an algorithm implementing the unique-id abstraction from bounded-storage registers maintaining read, write, and FAI operations. Given k registers, storing w bits each, our implementation generates up to (k - 1) · 2w unique identifiers, assuming that k ≤ 2w + 1. We show that this is asymptotically optimal: no unique-id implementation can produce more than k · 2w + k + 1 identifiers.

A recent approach to building consensus protocols on top of Directed Acyclic Graphs (DAGs) shows much promise due to its simplicity and stable throughput. However, as each node in the DAG typically includes a linear number of references to the nodes in the previous round, prior DAG protocols only scale up to a certain point when the overhead of maintaining the graph becomes the bottleneck. To enable large-scale deployments of DAG-based protocols, we propose a sparse DAG architecture, where each node includes only a constant number of references to random nodes in the previous round. We present a sparse version of Bullshark - one of the most prominent DAG-based consensus protocols - and demonstrate its improved scalability. Remarkably, unlike other protocols that use random sampling to reduce communication complexity, we manage to avoid sacrificing resilience: the protocol can tolerate up to f < n/3 Byzantine faults (where n is the number of participants), same as its less scalable deterministic counterpart. The proposed "sparse" methodology can be applied to any protocol that maintains disseminated system updates and causal relations between them in a graph-like structure. Our simulations show that the considerable reduction of transmitted metadata in sparse DAGs results in more efficient network utilization and better scalability.