In real-time systems, correct information is needed fast, so developing fast and accurate algorithms is a must. Algorithms must be resilient to transient faults and topology changes. The capability to adapt to heterogeneous and changing requirements is the core of assurance in distributed systems.

A snap-stabilizing algorithm, starting from an arbitrary system configuration, always behaves according to its specification.

In this paper, we propose a snap-stabilizing k-wave algorithm (called, kW) implementing k distinct consecutive waves (k > 2) for trees, with 0(h) rounds of delay and at most k + 4 states per process. The leaf nodes use only four states. The algorithm is optimal with respect to its time and state space complexity, and it can be generalized to arbitrary networks using any of the existing self-stabilizing spanning tree construction algorithms.