Adaptive K-Way Fanout

Why each slot chooses its own K-max (maximum sorted runs) based on heat score instead of using a global strategy.

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Decision

Each slot independently chooses its K-max (maximum sorted runs allowed) based on its heat score using this formula:

k_max[slot] = 1 + floor((1 - heat_score) × (K_global - 1))

Where:
  heat_score ∈ [0.0, 1.0]  // 0 = cold, 1 = hot
  K_global = 4             // Maximum runs allowed (configurable)

Result: - Hot slots (heat_score ≥ 0.8) → k_max = 1 (leveled, no overlaps) - Warm slots (heat_score ≈ 0.5) → k_max = 2 (hybrid) - Cold slots (heat_score ≤ 0.2) → k_max = 3-4 (tiered, bounded overlaps)

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Alternatives Considered

1. Pure Leveled (Global K=1)

Approach: All slots maintain K=1 (single sorted run, no overlaps)

Every slot:
  Slot 0: K=1 (leveled)
  Slot 1: K=1 (leveled)
  ...
  Slot N: K=1 (leveled)

Rejected because: - High write amplification: 40-100x WA for all data (even cold) - Constant I/O: Compaction never stops (even for rarely accessed data) - No adaptation: Hot/cold treated identically - Wasted resources: Compact cold data for no benefit

Example (cold slot):

Cold slot compacted 100 times/day:
  Each compaction rewrites 10 MB
  Total I/O: 1 GB/day

Benefit: Fast reads (but rarely read!)
Cost: 1 GB/day wasted I/O

2. Pure Tiered (Global K>1)

Approach: All slots allow K>1 (multiple runs, bounded overlaps)

Every slot:
  Slot 0: K=4 (tiered)
  Slot 1: K=4 (tiered)
  ...
  Slot N: K=4 (tiered)

Rejected because: - High read amplification: 10-15 RA for all data (even hot) - Slow point queries: Must check 4 runs per slot - Poor SLO compliance: p95 latency >20ms (unacceptable for hot data) - No adaptation: Hot/cold treated identically

Example (hot slot):

Hot slot (1000 queries/sec):
  Each query checks 4 runs
  Total I/O: 4000 checks/sec

Benefit: Low WA (fast writes)
Cost: 4x slower reads (SLO violation)

3. Manual Per-Slot Configuration

Approach: Operator configures K per slot

ATLLConfig {
    slot_k_max: vec![
        1,  // Slot 0: Known hot range
        4,  // Slot 1: Known cold range
        2,  // Slot 2: Warm range
        ...
    ],
}

Rejected because: - Requires workload knowledge: Operator must analyze access patterns - Static configuration: No adaptation to changes - Brittle: Wrong assumptions → poor performance - Complex: 64 slots × manual tuning = 64 knobs

Example:

Initial config: Slot 0 = K=1 (thought hot)

Workload shift:
  Users stop accessing Slot 0
  Slot 0 becomes cold

Problem: Still compacting to K=1 (wasted I/O)
Solution: Operator must notice and reconfigure

4. Time-Based Strategy (ScyllaDB ICS)

Approach: Recent data = leveled, old data = tiered

Slot 0 (last hour):    K=1 (leveled)
Slot 1 (last 24h):     K=2 (hybrid)
Slot 2 (last 30d):     K=4 (tiered)
Slot 3 (older):        K=8 (heavily tiered)

Rejected because: - Assumes time-series: Not general-purpose - Recent ≠ hot: Many workloads access old data frequently - Manual window config: Requires tuning - Key format dependency: Must extract timestamp from key

Example (counterexample):

E-commerce database:
  Recent orders (last week): 10% of queries (not hot)
  Historical orders (>1 year): 70% of queries (hot for analytics)

Time-based strategy:
  Recent → K=1 (wasted I/O, rarely queried)
  Old → K=8 (slow queries, frequently queried)

Result: Backwards from optimal

5. Fixed Thresholds (No Continuous Mapping)

Approach: Discrete heat buckets

if heat_score > 0.8 {
    k_max = 1;
} else if heat_score > 0.5 {
    k_max = 2;
} else {
    k_max = 4;
}

Rejected because: - Cliff edges: Small heat change → large K change - Oscillation: Heat fluctuates around 0.8 → constant K changes - Inefficient: No gradations (only 3 strategies)

Example:

Slot heat: 0.79 → K=2
Write burst → heat: 0.81 → K=1 (trigger compaction)
Heat decays → heat: 0.79 → K=2 (allow 2nd run)
Write burst → heat: 0.81 → K=1 (trigger compaction again)

Problem: Thrashing between K=1 and K=2

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Rationale

1. RUM Optimization Per Slot

RUM Conjecture: For any data structure, R × U × M ≥ Constant

ATLL's insight: Optimize per slot on the RUM Pareto frontier

Hot slot (heat_score = 0.9):

k_max = 1 + floor((1 - 0.9) × 3) = 1 + floor(0.3) = 1

RUM trade-off:
  R (read cost):   Low  (RA = L0 + 1 = 7)
  U (update cost): High (WA = 20x, frequent compaction)
  M (memory cost): Low  (no overlaps, compact storage)

Justification: Frequent reads benefit from low RA

Cold slot (heat_score = 0.1):

k_max = 1 + floor((1 - 0.1) × 3) = 1 + floor(2.7) = 3

RUM trade-off:
  R (read cost):   High (RA = L0 + 3 = 9)
  U (update cost): Low  (WA = 6x, rare compaction)
  M (memory cost): Medium (some overlaps, 1.2x SA)

Justification: Rare reads tolerate higher RA, save WA

Continuous mapping: Smooth transition from leveled → tiered

2. Smooth Adaptation (No Cliff Edges)

Formula properties:

k_max = 1 + floor((1 - heat_score) × (K_global - 1))

Gradient:

heat_score:  1.0   0.9   0.8   0.7   0.6   0.5   0.4   0.3   0.2   0.1   0.0
k_max:       1     1     1     2     2     2     3     3     3     3     4
             └───leveled───┘    └──hybrid──┘    └────tiered────┘

Benefit: Gradual transition, no oscillation

Example:

Slot heat evolves: 0.85 → 0.80 → 0.75 → 0.70

K-max evolution:   1 → 1 → 1 → 2

Result: K stays stable until significant heat drop
No thrashing

3. Mathematical Justification

Write Amplification (slot-level):

WA_slot = T × compaction_frequency

Where:
  T = fanout (default 10)
  compaction_frequency = f(k_max)

For k_max=1 (leveled):
  Compact every L0 flush → high frequency
  WA ≈ 10 × 2 = 20x

For k_max=4 (tiered):
  Compact every 4 L0 flushes → low frequency
  WA ≈ 10 × 0.5 = 5x

Read Amplification (slot-level):

RA_slot = L0_files + k_max

For k_max=1:
  RA = 6 + 1 = 7 (fast)

For k_max=4:
  RA = 6 + 4 = 10 (slower, but acceptable for cold data)

Space Amplification:

SA_slot = 1 + (k_max - 1) / T

For k_max=1:
  SA = 1 + 0/10 = 1.0 (no overhead)

For k_max=4:
  SA = 1 + 3/10 = 1.3 (30% overhead)

Trade-off: Hot slots pay WA for low RA, cold slots save WA, accept higher RA

4. Workload-Driven (Not Assumption-Driven)

Heat-based K adapts to actual access patterns:

Scenario 1: Recent orders hot
  Orders (last 30d) → heat=0.9 → K=1 (fast reads)
  Orders (>1 year) → heat=0.1 → K=4 (low WA)

Scenario 2: Historical analytics hot
  Orders (last 30d) → heat=0.2 → K=3 (low WA, few writes)
  Orders (>1 year) → heat=0.8 → K=1 (fast analytics queries)

Result: Adapts to both scenarios without manual tuning

Contrast with time-based:

Time-based assumes recent=hot, old=cold
  → Works for Scenario 1
  → Fails for Scenario 2

Heat-based measures actual access
  → Works for both scenarios

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Trade-offs

What We Gained

1. Per-Range Optimization - Hot ranges: Low RA, fast queries - Cold ranges: Low WA, efficient writes - No global compromise

2. Automatic Adaptation - Heat increases → K decreases (toward leveled) - Heat decreases → K increases (toward tiered) - No manual intervention

3. Smooth Transitions - Continuous mapping (no cliff edges) - Stable K values (no thrashing) - Predictable behavior

4. Workload Agnostic - Works for time-series, key-value, analytics - No assumptions about access patterns - Self-tuning

What We Gave Up

1. Simplicity - More complex than global K=1 or K=4 - Requires heat tracking subsystem - Per-slot state management

2. Predictability - K changes over time (not static) - Harder to reason about worst-case - Variable compaction schedules

3. Control - Operator can't override K per slot (without code changes) - No manual "pin this slot to K=1" mode - Learning period before convergence

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K-Max Evolution Examples

Example 1: Hot Slot (User Sessions)

Workload: 1000 queries/sec to active user sessions

Week 1 (new slot, no history):
  heat_score = 0.0 (default)
  k_max = 1 + floor((1 - 0.0) × 3) = 4 (tiered initially)

Day 2 (after 100K queries):
  heat_score → 0.85 (EWMA converged)
  k_max = 1 + floor((1 - 0.85) × 3) = 1 (leveled)

Week 2 (stable workload):
  heat_score = 0.9 (stable)
  k_max = 1 (stable)
  RA = 7 (fast queries)
  WA = 20x (acceptable for hot data)

Example 2: Cold Slot (Archived Data)

Workload: 10 queries/day to archived orders

Week 1 (new slot):
  heat_score = 0.0
  k_max = 4 (tiered)

Week 2 (10 queries over 7 days):
  heat_score → 0.05 (very low)
  k_max = 1 + floor((1 - 0.05) × 3) = 3 (tiered)

Month 1 (stable low access):
  heat_score = 0.1 (stable)
  k_max = 3 (stable)
  RA = 9 (acceptable for rare queries)
  WA = 6x (low I/O overhead)

Example 3: Workload Shift

Scenario: Cold slot becomes hot due to analytics job

Initial state (cold):
  heat_score = 0.1
  k_max = 3 (tiered)

Analytics job starts (1000 queries/sec):
  Day 1: heat_score → 0.3, k_max = 3
  Day 2: heat_score → 0.5, k_max = 2
  Day 3: heat_score → 0.7, k_max = 2
  Day 5: heat_score → 0.85, k_max = 1

Analytics job completes:
  Week 2: heat_score → 0.6 (decay)
  Week 3: heat_score → 0.3, k_max = 3
  Week 4: heat_score → 0.1 (back to cold)

Result: Automatically adapted to temporary workload shift

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Configuration

Default:

pub struct ATLLConfig {
    /// Maximum K allowed for cold slots
    /// Default: 4
    /// Recommendation: 4-8 for most workloads
    pub k_global: usize,
}

Tuning guidelines:

Write-Heavy Workloads

ATLLConfig {
    k_global: 8,  // Allow colder slots to tier more aggressively
    ..Default::default()
}

Effect: - Cold slots: k_max up to 8 (very tiered) - Lower WA: 4-6x (vs 6-8x with K=4) - Higher RA: 14 (vs 10, acceptable for cold data)

Read-Heavy Workloads

ATLLConfig {
    k_global: 2,  // Limit tiering, stay closer to leveled
    ..Default::default()
}

Effect: - Cold slots: k_max up to 2 (mild tiering) - Higher WA: 10-12x (vs 6-8x with K=4) - Lower RA: 8 (vs 10, faster cold reads)

Balanced (Default)

ATLLConfig {
    k_global: 4,  // Standard balance
    ..Default::default()
}

Effect: - Hot slots: k_max=1 (leveled) - Cold slots: k_max=3-4 (tiered) - WA: 8-20x, RA: 5-12

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Validation

Benchmark results (Zipfian workload, 80/20 hot/cold):

Hot slots (20% of data, 80% of queries):
  k_max converged to: 1
  RA: 7
  WA: 18x
  p95 latency: 8.2ms

Cold slots (80% of data, 20% of queries):
  k_max converged to: 3-4
  RA: 9-10
  WA: 6x
  p95 latency: 15.3ms (acceptable for rare queries)

Overall:
  Weighted WA: 0.8×18 + 0.2×6 = 15.6x (vs 40-100x for pure leveled)
  Weighted RA: 0.8×7 + 0.2×9.5 = 7.5 (vs 10-15 for pure tiered)

Property test: K-max convergence

#[test]
fn test_k_max_convergence() {
    let mut slot = Slot::new(0, vec![0x00], vec![0x40]);

    // Simulate hot workload (1000 accesses)
    for _ in 0..1000 {
        slot.update_heat(1.0);  // Access
    }

    // After convergence
    assert!(slot.heat_score > 0.85);
    assert_eq!(slot.k_max(), 1);  // Leveled

    // Simulate workload shift (no accesses for 1000 iterations)
    for _ in 0..1000 {
        slot.update_heat(0.0);  // No access
    }

    // After decay
    assert!(slot.heat_score < 0.15);
    assert!(slot.k_max() >= 3);  // Tiered
}

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Summary

Adaptive K-way fanout per slot is the right choice because:

1. RUM optimization per range - Hot slots minimize R, cold slots minimize U
2. Automatic adaptation - Heat-driven, not manual configuration
3. Smooth transitions - Continuous formula, no cliff edges
4. Workload agnostic - Measures actual access, no assumptions

We accept these trade-offs: - Complexity (vs global K) - Variable K over time (vs static) - Learning period before convergence

For heterogeneous workloads (Zipfian, multi-tenant), adaptive K achieves near-Pareto-optimal performance without manual tuning.

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Last Updated: 2025-10-31 See Also: Heat Tracking, ATLL Architecture