Kaspa computes block relations efficiently using a parallelized DAG traversal system combined with the GHOSTDAG ordering algorithm. Instead of comparing every block with every other block, Kaspa uses incremental parent references, topological ordering, k-cluster scoring, and local conflict detection to calculate relationships in real time. This allows Kaspa to process one block per second while maintaining secure, deterministic consensus.
What Makes Block Relation Computation Hard in a DAG?
On a classic blockchain, each block has exactly one parent, so relations are simple:
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Parent → Child
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Older → Newer
In a blockDAG, multiple blocks arrive simultaneously.
Each block may reference several parents, forming a web of relations:
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Ancestors
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Descendants
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Siblings
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Conflicts
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Merging paths
Naively computing these relations would require full graph scans, which would be slow and unscalable.
Kaspa solves this with smart mathematical data structures.
1. Efficient Parent References (Immediate Relation Computation)
Each Kaspa block contains multiple parent pointers.
From these parents, Kaspa immediately knows:
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Its direct ancestors
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The blue/red status of parent clusters
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The relative scoring weight
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Whether the block conflicts with others
Because the DAG is always topologically sorted, Kaspa uses these references to compute relations in O(1) to O(log n) complexity.
Why this matters
Kaspa avoids re-scanning historical blocks.
Instead, every block carries the metadata needed to compute its relationships instantly.
2. Topological Ordering: Kaspa’s Backbone of Efficiency
Kaspa maintains a topologically sorted DAG, meaning:
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Every parent appears before its child
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No cycles exist
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The order is deterministic
This allows:
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Fast traversal
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Instant ancestor/descendant checks
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Efficient conflict detection
Kaspa uses incremental topological updates, not full graph reordering.
This keeps the system lightweight even at high block rates.
3. GHOSTDAG’s k-Cluster Algorithm Reduces Comparison Work
Instead of comparing every block with every other block, GHOSTDAG:
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Forms a blue cluster (honest blocks)
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Allows up to k red conflicts
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Scores and orders blocks based on connectivity
Because k is bounded, the algorithm knows:
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How many comparisons it must make
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Which subgraph to focus on
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Which relations are relevant
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Which blocks are safe to ignore in scoring
This is mathematically efficient and highly scalable.
4. Localized Conflict Detection
Kaspa checks conflicts locally, not globally.
A new block is compared only against:
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Its parents
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The parents’ siblings
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The k-conflict window
Kaspa never scans the entire DAG to detect conflicts.
This makes relation computation extremely fast, even as the DAG grows large.
5. HashMaps + Set Structures for Instant Lookups
Kaspa stores:
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Ancestors
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Blue score
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Merge sets
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Relations
in HashMaps, enabling:
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O(1) access
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Constant-time relation checks
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Fast conflict lookups
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Efficient block scoring
The DAG is backed by a highly optimized, memory-efficient set of relational structures.
6. Pruned Merge Sets (PMS): Kaspa’s Smart Optimization
Kaspa stores a compressed representation of a block’s merge-set.
A merge-set is essentially:
All blocks that are reachable but not ancestors.
Computing this naively is expensive.
Kaspa uses Pruned Merge Sets (PMS) to track only important relations.
This enables:
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Quick conflict detection
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Fast k-cluster checks
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Efficient DAG traversal
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Minimal memory consumption
This is one of Kaspa’s most important scaling techniques.
7. Blue Score Propagation
Kaspa assigns a blue score to each block, which represents:
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Its weight
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Its connectedness
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How “deep” it is in the canonical DAG
Instead of recalculating blue scores from scratch:
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Each new block inherits scores from parents
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Scores update incrementally
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Only a small subset of blocks is evaluated
This dramatically speeds up consensus calculations.
8. Parallelized DAG Computation
Kaspa’s design enables parallel processing:
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Blocks can be validated simultaneously
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Relations are computed in parallel threads
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GHOSTDAG ordering runs concurrently with network propagation
The DAG naturally supports concurrency because it inherently represents parallelism.
This is a major advantage over linear blockchains.
Conclusion
Kaspa’s DAG is fast because it uses incremental, bounded, and localized computation.
Kaspa combines:
✔ Topological ordering
✔ Fast parent-pointer traversal
✔ k-cluster bounded conflict resolution
✔ HashMaps for constant-time lookup
✔ Pruned merge-set structures
✔ Parallelized DAG processing
This allows Kaspa to compute block relations at one block per second while remaining:
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Deterministic
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Secure
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Scalable
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Efficient
Kaspa turns graph theory into real performance.