A one-round next-higher-ID neighbor selection rule achieves backup placement with load at most c in graphs of neighborhood independence c, and enables a (2+epsilon)-approximate maximum matching in O(log* n) rounds.
Distributed backup placement in networks
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Distributed Backup Placement in One Round and its Applications to Maximum Matching Approximation and Self-Stabilization
A one-round next-higher-ID neighbor selection rule achieves backup placement with load at most c in graphs of neighborhood independence c, and enables a (2+epsilon)-approximate maximum matching in O(log* n) rounds.