Why it matters

Persistent DSU enables versioned queries. Understanding shapes offline algorithms.

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The architecture

Store parent + rank per version.

Path-copying or fat-node persistence.

Query historical connectivity.

Persistent DSU structureVersioned stateper union / findPath-copyinglog n per opQuery any versionhistorical connectivityApplications: offline dynamic connectivity + geometric algorithms
Persistent DSU.
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How it works end to end

Path-copying or fat-node.

O(log n) per op typical.

Applications: offline dynamic connectivity.