Finding a provably correct subquadratic synchronization algorithm for many filesystem replicas is one of the main theoretical problems in operational transformation (OT) and conflict-free replicated data types (CRDT) frameworks. Based on algebraic theory filesystems, which incorporates non-commutative commands natively, we developed built proof-of-concept implementation an suite synchronizes ar...

Let G be a connected graph with maximum degree Δ≥3 distinct from KΔ+1. Generalizing Brooks’ Theorem, Borodin and independently Bollobás Manvel, proved that if p1,…,ps are non-negative integers such p1+⋯+ps≥Δ−s, then admits vertex partition into parts A1,…,As that, for 1≤i≤s, G[Ai] is pi-degenerate. Here we show can performed in time O(n+m). This generalizes previous results treated subcases of ...