New graph sketches cut verification data by 100x in CONGEST networks

Locally Checkable Proofs-with-Errors (LCPE) allow distributed networks to verify global properties despite corrupted certificates. Until now, LCPE algorithms targeted the LOCAL model, where nodes can exchange arbitrarily large messages. For bandwidth-constrained CONGEST networks, the naive approach would require each node to communicate the exact topology of its (2ε+1)-hop neighborhood—costing up to O(Δ^{2ε+1} log n) bits.

This work from Garncarek et al. overcomes that bottleneck by compressing neighborhood information into local graph sketches of just O(ε² log n) bits. Using the novel concepts of imagined trees and imagined certifications, each node can independently verify that a unique leader exists, even when up to ε certificates are adversarially corrupted. The algorithm runs in O(ε²) CONGEST rounds, a dramatic improvement. The authors also prove a tight lower bound: no scheme with view distance ≤ ε can tolerate ε errors, even in the LOCAL model—showing their approach is essentially optimal.

The result has immediate implications for fault-tolerant distributed systems, enabling efficient leader verification in IoT, sensor networks, and blockchain layers where bandwidth is at a premium. It also opens new avenues for graph-sketching techniques in distributed verification.