Researchers crack distributed graph coloring with new algorithm
New algorithm solves graph coloring in O(log n) rounds without network diameter dependency
Deep Dive
Amit Nir and David Peleg introduced two randomized proper-coloring algorithms for the synchronous CONGEST model that control color frequencies without a diameter-dependent coordination cost. For any fixed δ > 0, the first algorithm uses χ = ⌈(2+δ)Δ⌉ colors and, with probability at least 1 − n^(−λ), bounds every color frequency’s deviation from n/χ by O_δ(√((λ+1)(n/χ) log n) + (λ+1) log n); under an explicit load condition, this yields two-sided relative balance. The second algorithm works for every χ > Δ
Key Points
- Two randomized graph coloring algorithms eliminate diameter-dependent coordination costs in distributed networks
- First algorithm uses (2+δ)Δ colors with O(√n lg n) frequency deviation guarantee
- Both algorithms achieve O((λ+1) lg n) round complexity, removing network diameter dependency
Why It Matters
Enables scalable graph algorithms in large distributed systems where network diameter is unpredictable or large