Concurrent node joins and Stabilization Παρουσίαση: Νίκος Κρεμμυδάς Πάνος Σκυβαλίδας

Stabilization Correctness of lookups guaranteed by “stabilization” protocol used to keep successor pointers up to date. Finger tables can always be verified. Each node runs “stabilization” protocol, periodically, to update successors and finger tables.

Lookup issue Lookup before stabilization has finished  Finger table entries reasonably current: Lookup finds correct successor in O(logN) steps.  Successor pointers correct but fingers inaccurate: Correct lookups but slower.  Incorrect successor pointers or incorrect mapping (keys to nodes): Lookup may fail, higher layer software retries lookup optionally.

Stabilization algorithm (1/2) “Stabilization” protocol:  join()  stabilize()  notify()  fix_fingers()

Stabilization algorithm (2/2) When n joins, it calls join(n’) where n’ any node. join asks n’ to find immediate successor of n. Every node runs stabilize() periodically When n runs stabilize(), it asks n’s successor for successor’s predecessor p and decides whether p should be n’s successor. notify(n) notifies n’s successor k of n’s existence, so that n becomes k’s predecessor (only if k knows not of a closer predecessor). fix_fingers() adjusts old nodes’ finger table entries and initializes new nodes’ finger tables.

Stabilization example

Stabilization theorems THEOREM 4. Once a node can successfully resolve a given query, it will always be able to do so in the future. THEOREM 5. At some time after the last join all successor pointers will be correct. THEOREM 6. If we take a stable network with n nodes, and another set of up to n nodes joins the network with no finger pointers (but with correct successor pointers), then lookups will still take O(logN) time with high probability.

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