Fast Deterministic Distributed Degree Splitting
A new deterministic algorithm achieves O(ε⁻¹·log n) complexity for degree splitting, beating prior state-of-the-art.
A team of computer scientists—Yannic Maus, Alexandre Nolin, and Florian Schager—has published a preprint titled 'Fast Deterministic Distributed Degree Splitting' that presents a significant algorithmic advance for distributed graph problems. Their work introduces a new deterministic algorithm that computes a balanced orientation of edges in a graph, ensuring that for every vertex v, the difference between its incoming and outgoing edges (the discrepancy) is at most ε times its degree. This is achieved in O(ε⁻¹·log n) communication rounds within the standard LOCAL model of distributed computing. This result marks a clear improvement over the previous best-known algorithm from 2020, which had a more complex runtime of O(ε⁻¹·log ε⁻¹·(log log ε⁻¹)¹.⁷¹·log n).
The core innovation lies in establishing a connection to the hypergraph sinkless orientation problem, a known hard problem in distributed computing. By leveraging this connection, the authors not only streamline the algorithm for balanced orientations but also extend it to compute undirected degree splits with the same efficiency. This theoretical advancement has immediate practical applications. As demonstrated, it can be used to solve the (3/2+ε)Δ-edge coloring problem—assigning colors to edges so that adjacent edges have different colors—in O(ε⁻¹·log² Δ·log n + ε⁻²·log n) rounds. Notably, for constant ε and moderately growing maximum degree Δ, this runtime matches the current state-of-the-art for the simpler (2Δ-1)-edge coloring problem, indicating a major step toward optimal distributed graph coloring algorithms.
This work, submitted to the Principles of Distributed Computing (PODC) 2026 conference, represents a fundamental improvement in the toolkit for designing efficient, deterministic distributed algorithms. By providing a faster and simpler method for a core graph-balancing primitive, it paves the way for more efficient solutions in large-scale network coordination, parallel computation, and resource allocation where graph structures are paramount.
- Achieves O(ε⁻¹·log n) runtime for degree splitting, improving on prior O(ε⁻¹·log ε⁻¹·(log log ε⁻¹)¹.⁷¹·log n) result.
- Enables (3/2+ε)Δ-edge coloring in O(ε⁻¹·log² Δ·log n + ε⁻²·log n) rounds, matching state-of-the-art for simpler problems.
- Based on a novel connection to the hypergraph sinkless orientation problem, simplifying the algorithm design.
Why It Matters
Enables faster, more deterministic coordination in massive distributed systems like cloud networks and parallel supercomputers.