New algorithm solves graph edge coloring in CONGEST model
First deterministic poly(log n)-round solution for Δ+1-edge coloring in CONGEST
Deep Dive
A new paper by Sebastian Brandt, Ananth Narayanan, and Alexandre Nolin presents the first deterministic poly(Δ, log n)-round algorithm for (Δ+1)-edge coloring in the CONGEST model. Its n-dependency is Õ(log⁵ n), matching the best published dependency in the LOCAL model. This answers an open question left by previous LOCAL algorithms, which relied on large messages.
Key Points
- First deterministic poly(log n)-round algorithm for (Δ+1)-edge coloring in CONGEST model
- Runtime of Õ(log⁵ n) rounds matches best LOCAL model solutions despite stricter communication constraints
- Solves open problem from Bernshteyn (2022) and subsequent works that relied on large messages
Why It Matters
Enables efficient distributed graph algorithms in bandwidth-limited networks, crucial for large-scale computing and networking applications.