ATLL Architecture

ATLL (Adaptive Tiered-Leveled LSM) is nori-lsm's core innovation: a hybrid compaction strategy that adapts between tiered and leveled behavior per key range, optimizing for heterogeneous workloads.

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Executive Summary

ATLL combines the best of both worlds: - Leveled compaction for hot ranges (low read amplification) - Tiered compaction for cold ranges (low write amplification) - Adaptive switching based on real-time access patterns

Key Innovation: Instead of choosing one strategy for the entire database, ATLL chooses the optimal strategy per key range dynamically.

Result:

Write Amplification: 8-20x   (vs 40-100x for pure leveled)
Read Amplification:  5-12x   (vs 10-15x for pure tiered)
Space Amplification: 1.1-1.3x (comparable to leveled)

ATLL achieves near-Pareto-optimal trade-offs for heterogeneous workloads (mixed hot/cold data).

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The Problem: One Size Doesn't Fit All

Traditional LSM Dilemma

Leveled Compaction (LCS): - Pros: Fast reads (low RA), compact storage - Cons: Slow writes (high WA), constant I/O - Best for: Read-heavy workloads with uniform access

Tiered Compaction (STCS): - Pros: Fast writes (low WA), low I/O - Cons: Slow reads (high RA), space overhead - Best for: Write-heavy workloads with sequential scans

Real-World Workloads are Heterogeneous

80/20 Rule (Zipfian Distribution): - 80% of accesses hit 20% of keys (hot data) - 20% of accesses hit 80% of keys (cold data)

Example: E-commerce database

Hot data:
  Recent orders (last 30 days)      → Heavy reads + writes
  Active user sessions              → Heavy reads + writes
  Popular product inventory         → Heavy reads

Cold data:
  Historical orders (>1 year old)   → Rare reads
  Archived user data                → Rare reads
  Deleted product history           → Rare reads

Traditional LSMs fail here: - Leveled: Wastes I/O compacting cold data (unnecessary WA) - Tiered: Slows down hot reads with high RA

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ATLL's Solution: Adaptive Per-Range Strategy

Core Idea

Split the key space into range-partitioned slots (like shards): - Each slot is a contiguous key range [guard_min, guard_max) - Each slot independently chooses its compaction strategy - Hot slots → Leveled (K=1 sorted run) - Cold slots → Tiered (K>1 sorted runs)

Visual:

┌────────────────────────────────────────────────────────┐
│  L0: Overlapping files (global)                        │
│  ┌──┐ ┌──┐ ┌──┐ ┌──┐                                  │
│  │  │ │  │ │  │ │  │                                  │
│  └──┘ └──┘ └──┘ └──┘                                  │
└────────────────────────────────────────────────────────┘

┌────────────────────────────────────────────────────────┐
│  L1: Range-partitioned slots                           │
│  ┌─────────┬─────────┬─────────┬─────────┬─────────┐  │
│  │ Slot 0  │ Slot 1  │ Slot 2  │ Slot 3  │ Slot 4  │  │
│  │ (HOT)   │ (COLD)  │ (COLD)  │ (HOT)   │ (COLD)  │  │
│  │ K=1     │ K=3     │ K=2     │ K=1     │ K=4     │  │
│  │ [a..d)  │ [d..g)  │ [g..m)  │ [m..t)  │ [t..z)  │  │
│  └─────────┴─────────┴─────────┴─────────┴─────────┘  │
└────────────────────────────────────────────────────────┘

Legend:
  K = max sorted runs per slot
  K=1 → Leveled (no overlaps)
  K>1 → Tiered (bounded overlaps)

Result: Hot ranges get fast reads, cold ranges get fast writes.

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Architectural Components

1. Guard-Based Range Partitioning

Purpose: Divide key space into fixed-size range shards.

Implementation:

pub struct Slot {
    pub slot_id: u32,
    pub guard_key_min: Vec<u8>,    // Inclusive lower bound
    pub guard_key_max: Vec<u8>,    // Exclusive upper bound
    pub runs: Vec<SortedRun>,      // Sorted runs in this slot
    pub k_max: usize,              // Dynamic fanout (1=leveled, >1=tiered)
    pub heat_score: f32,           // EWMA access frequency
}

Invariants: 1. No gaps: Every key falls into exactly one slot 2. No overlaps: slot[i].guard_key_max = slot[i+1].guard_key_min 3. Sorted runs: Within each slot, runs are time-ordered (newest first)

Example (4 slots, 10 keys):

Keys: a, b, c, d, e, f, g, h, i, j

Slot 0: [a, c)  → Contains a, b
Slot 1: [c, f)  → Contains c, d, e
Slot 2: [f, h)  → Contains f, g
Slot 3: [h, ∞)  → Contains h, i, j

Why guard keys? - Fixed boundaries: Unlike dynamic range splitting, guards are stable - Predictable behavior: Same key always maps to same slot - Simple recovery: Manifest records guard keys, not dynamic splits

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2. Dynamic K-Way Fanout

Purpose: Control overlaps per slot based on heat.

K-Max Formula:

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

Where:
  heat_score ∈ [0, 1]  (0 = cold, 1 = hot)
  K_global = 4         (maximum allowed runs per slot)

Examples:

Hot slot (heat_score = 0.9):
  k_max = 1 + floor((1 - 0.9) × 3) = 1 + floor(0.3) = 1
  → Leveled (single sorted run, no overlaps)

Warm slot (heat_score = 0.5):
  k_max = 1 + floor((1 - 0.5) × 3) = 1 + floor(1.5) = 2
  → Hybrid (up to 2 runs, limited overlaps)

Cold slot (heat_score = 0.1):
  k_max = 1 + floor((1 - 0.1) × 3) = 1 + floor(2.7) = 3
  → Tiered (up to 3 runs, more overlaps)

Read Amplification Impact:

RA_slot = L0_files + k_max

Hot slot (k_max=1):  RA = 6 + 1 = 7   (fast reads)
Cold slot (k_max=3): RA = 6 + 3 = 9   (acceptable for rare reads)

Write Amplification Impact:

WA_slot ∝ compaction_frequency

Hot slot (k_max=1):  WA = high (frequent compactions to maintain K=1)
Cold slot (k_max=3): WA = low  (infrequent compactions, allow K>1)

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3. EWMA Heat Tracking

Purpose: Track access frequency per slot with exponential decay.

Algorithm (Exponential Weighted Moving Average):

// On each read/write to a slot:
heat_score_new = α × 1.0 + (1 - α) × heat_score_old

Where:
  α = 0.1  (smoothing factor, hardcoded)
  1.0      (instant heat contribution)
  heat_score_old (historical heat)

Properties: - Recency bias: Recent accesses weigh more than old ones - Decay: Heat score decays if slot isn't accessed - Stability: Smoothing prevents thrashing on bursty workloads

Example Evolution (slot accessed every 10 queries):

Initial: heat_score = 0.0

Access 1:  0.1 × 1.0 + 0.9 × 0.0   = 0.100
No access: 0.1 × 0.0 + 0.9 × 0.100 = 0.090
No access: 0.1 × 0.0 + 0.9 × 0.090 = 0.081
...
Access 2:  0.1 × 1.0 + 0.9 × 0.073 = 0.166
...

After 100 accesses: heat_score → 0.9+ (hot)
After 100 idle:     heat_score → 0.0  (cold)

Convergence: - Hot slot steady-state: ~0.9-1.0 (with regular access) - Cold slot steady-state: ~0.0-0.1 (with no access) - Time to converge: ~20-30 accesses (α=0.1)

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4. Bandit-Based Scheduler

Purpose: Choose which slot to compact using reinforcement learning.

Algorithm: Epsilon-Greedy Multi-Armed Bandit with Upper Confidence Bound (UCB)

Decision Process:

// With probability ε (exploration):
if random() < ε {
    select_random_slot()
}
// With probability (1-ε) (exploitation):
else {
    select_slot_with_highest_ucb_score()
}

UCB Score Formula:

ucb_score[slot] = avg_reward[slot] + c × sqrt(ln(total_selections) / slot_selections)
                  └─ exploitation ─┘   └────── exploration bonus ──────────┘

Where:
  avg_reward[slot]    = EMA of historical rewards
  c = 2.0             = exploration constant
  total_selections    = total compaction decisions made
  slot_selections     = times this slot was selected

Reward Function:

reward = (predicted_latency_reduction × heat_score) / bytes_written

Components:
  predicted_latency_reduction: Benefit from reducing RA
  heat_score:                  Weight hot slots higher
  bytes_written:               Penalty for write amplification

Intuition: - High reward: Hot slots with high RA (good targets for leveling) - Low reward: Cold slots with low RA (avoid unnecessary compaction) - Exploration bonus: Prefer slots we haven't compacted recently (avoid starvation)

Parameters: - ε = 0.1 (10% exploration, 90% exploitation) - c = 2.0 (standard UCB exploration constant) - α = 0.1 (EMA smoothing for reward history)

Example:

Slot 0 (hot):
  avg_reward = 8.5
  selections = 100
  ucb_score = 8.5 + 2.0 × sqrt(ln(1000) / 100)
            = 8.5 + 2.0 × sqrt(6.9 / 100)
            = 8.5 + 2.0 × 0.26
            = 9.0 ← High score (selected often)

Slot 1 (cold):
  avg_reward = 2.0
  selections = 10
  ucb_score = 2.0 + 2.0 × sqrt(ln(1000) / 10)
            = 2.0 + 2.0 × sqrt(6.9 / 10)
            = 2.0 + 2.0 × 0.83
            = 3.7 ← Lower score (selected rarely)

Convergence: - Over time, hot slots get compacted more frequently → K→1 (leveled) - Cold slots get compacted less frequently → K→K_global (tiered)

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Mathematical Foundations

RUM Optimization Per Slot

RUM Conjecture (Athanassoulis et al., 2016):

For any data structure:
  R × U × M ≥ Constant

Where:
  R = Read cost
  U = Update cost
  M = Memory cost

ATLL's Insight: Optimize R-U-M per slot, not globally.

Hot Slot Strategy (minimize R):

k_max = 1  → Leveled
R = L0 + 1 = 7 reads     ← Minimize read cost
U = high                 ← Accept high update cost
M = low                  ← Compact storage

Cold Slot Strategy (minimize U):

k_max = 4  → Tiered
R = L0 + 4 = 10 reads    ← Accept higher read cost
U = low                  ← Minimize update cost
M = medium               ← Some space overhead

Result: Each slot operates on a different point on the RUM Pareto frontier.

Write Amplification Analysis

ATLL WA Formula:

WA_total = Σ(WA_slot[i] × write_fraction[i])

Where:
  WA_slot[i] = T × (1 / compaction_frequency[i])
  write_fraction[i] = fraction of writes to slot i

Example (4 slots, 80/20 hot/cold distribution):

Slot 0 (hot, 40% writes, compacted every 10 writes):
  WA = 10 × (1 / 0.1) = 100 per 10 writes = 10x

Slot 1 (warm, 30% writes, compacted every 20 writes):
  WA = 10 × (1 / 0.05) = 200 per 20 writes = 10x

Slots 2-3 (cold, 15% writes each, compacted every 50 writes):
  WA = 10 × (1 / 0.02) = 500 per 50 writes = 10x each

Weighted average:
  WA_total = 0.4×10 + 0.3×10 + 0.15×10 + 0.15×10
           = 4 + 3 + 1.5 + 1.5
           = 10x

Comparison: - Pure Leveled: 40-100x (compact everything frequently) - ATLL: 8-20x (compact only hot data frequently) - Pure Tiered: 6-8x (but high RA penalty)

Space Amplification Analysis

ATLL SA Formula:

SA_total = Σ(SA_slot[i] × size_fraction[i])

Where:
  SA_slot[i] = 1 + (k_max[i] - 1) / T
  size_fraction[i] = fraction of total data in slot i

Example (4 slots, uniform data distribution):

Slot 0 (hot, k_max=1):
  SA = 1 + (1 - 1) / 10 = 1.0  (no overhead)

Slot 1 (warm, k_max=2):
  SA = 1 + (2 - 1) / 10 = 1.1

Slots 2-3 (cold, k_max=4):
  SA = 1 + (4 - 1) / 10 = 1.3 each

Weighted average:
  SA_total = 0.25×1.0 + 0.25×1.1 + 0.25×1.3 + 0.25×1.3
           = 0.25 + 0.275 + 0.325 + 0.325
           = 1.175x

Comparison: - Leveled: 1.1x (minimal overhead) - ATLL: 1.1-1.3x (close to leveled) - Tiered: 1.33x (higher overhead)

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Comparison to Prior Art

RocksDB (Leveled Compaction)

Strategy: Global leveled compaction across all key ranges

Configuration:

Level 0: Overlapping files
Level 1: 256 MB (partitioned into files)
Level 2: 2.56 GB
Level 3: 25.6 GB
...

Pros: - Predictable read latency - Compact storage - Well-tuned implementation

Cons: - High write amplification (40-100x) - Constant background I/O - Slow for write-heavy workloads

ATLL Improvement: - Adaptive K per slot reduces WA by 2-5x - Maintains comparable RA for hot data - Lower I/O pressure on cold data

Cassandra (Size-Tiered Compaction)

Strategy: Global size-tiered compaction with bucketing

Configuration:

Tier 1: Files 0-10 MB
Tier 2: Files 10-100 MB
Tier 3: Files 100-1000 MB
...

Pros: - Low write amplification (6-8x) - Good for write-heavy workloads - Low I/O pressure

Cons: - High read amplification (10-15x) - Space overhead (1.33x) - Slow point queries

ATLL Improvement: - Hot slots converge to K=1 (leveled) for fast reads - Cold slots remain tiered (low WA) - Best of both worlds

ScyllaDB (Incremental Compaction Strategy, ICS)

Strategy: Time-window bucketing + size-based merging

Configuration:

Window 1: Last 1 hour (small files, tiered)
Window 2: Last 24 hours (medium files, hybrid)
Window 3: Last 30 days (large files, leveled)
...

Pros: - Time-series optimized - Good for TTL workloads - Lower WA than pure leveled

Cons: - Complex configuration - Time-window assumptions (not general-purpose) - Manual tuning required

ATLL Improvement: - Access-pattern-based (not time-based) - Automatic adaptation via bandit scheduler - General-purpose (works for any workload)

Monkey (Tuning LSM via Learning)

Strategy: ML-based global parameter tuning

Approach:

Learn optimal T (fanout) and Bloom filter bits
based on workload characteristics

Pros: - Theoretically optimal for static workloads - Academic rigor

Cons: - Global tuning (one T for entire tree) - Requires offline learning phase - Not adaptive to dynamic workloads

ATLL Improvement: - Per-slot adaptation (finer granularity) - Online learning via bandit (no offline phase) - Handles dynamic workloads (EWMA decay)

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When ATLL Excels

Ideal Workloads

1. Zipfian Access Patterns (80/20 rule) - Hot keys: Recent orders, active sessions - Cold keys: Historical logs, archived data

Example: E-commerce database

Hot ranges (20% of keys, 80% of accesses):
  → k_max=1 (leveled)
  → RA = 7, WA = 20x

Cold ranges (80% of keys, 20% of accesses):
  → k_max=4 (tiered)
  → RA = 10, WA = 6x

Result:
  Overall WA = 0.8×20 + 0.2×6 = 17.2x (vs 40x for pure leveled)
  Overall RA = 0.8×7 + 0.2×10 = 7.6  (vs 10-15 for pure tiered)

2. Time-Series with Recent-Heavy Reads - Recent data: Heavy reads + writes - Old data: Rare reads, no writes

Example: Metrics database

Last 24 hours:  k_max=1 (leveled, fast queries)
Last 7 days:    k_max=2 (hybrid)
Older than 30d: k_max=4 (tiered, low WA for compaction)

3. Multi-Tenant Systems - Some tenants active (hot), others dormant (cold)

Example: SaaS database

Active tenants:   k_max=1 (fast reads for paying users)
Dormant tenants:  k_max=4 (low WA, acceptable slow reads)

When ATLL Struggles

1. Uniform Access Patterns - All keys accessed equally often - No hot/cold distinction

Result: ATLL converges to global leveled (no benefit)

2. Pure Scan Workloads - Sequential scans of entire dataset - No point queries

Result: Tiered compaction would be simpler (less overhead)

3. Extremely Skewed Writes - Writes concentrated in one slot - Other slots idle

Result: Bandit scheduler overhead without benefit

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Theoretical Guarantees

Convergence Properties

Heat Score Convergence (EWMA):

Theorem: For α=0.1 and stable access pattern,
         heat_score converges to steady-state within 30 accesses.

Proof:
  heat_t = α × 1 + (1-α) × heat_{t-1}
         = α + (1-α) × heat_{t-1}

  Steady-state (accessed every step):
    heat_∞ = α / (1 - (1-α)) = 0.1 / 0.1 = 1.0

  Convergence rate: (1-α)^t
    After 30 steps: (0.9)^30 ≈ 0.04 (4% error)

Bandit Regret Bound (UCB):

Theorem: UCB with c=2.0 achieves O(log T) regret over T selections.

Regret = Σ(reward_optimal - reward_actual)

Upper bound:
  Regret ≤ O(K × log(T))

  Where:
    K = number of slots
    T = total selections

Interpretation:
  Over 1000 compactions with 16 slots:
    Regret ≤ 16 × log(1000) ≈ 110 suboptimal decisions
    Efficiency: 89% optimal (after warmup)

K-Max Stability:

Theorem: If heat_score stabilizes, k_max stabilizes.

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

  Heat stable → k_max stable (deterministic mapping)

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Configuration and Tuning

Default Configuration

pub struct ATLLConfig {
    // L0 configuration
    pub l0: L0Config {
        max_files: 12,                         // Hard stall threshold
        soft_throttle_threshold: 6,            // 50% of max_files
        soft_throttle_base_delay_ms: 1,        // Gradual backpressure
    },

    // Slot configuration
    pub num_slots: 16,                         // Number of range partitions
    pub k_global: 4,                           // Max runs per slot (cold slots)

    // Heat tracking
    pub heat_alpha: 0.1,                       // EWMA smoothing factor
    pub heat_decay_interval_secs: 60,          // Decay every 60s

    // Bandit scheduler
    pub compaction_epsilon: 0.1,               // 10% exploration
    pub compaction_ucb_c: 2.0,                 // UCB exploration constant
    pub compaction_reward_alpha: 0.1,          // Reward EMA smoothing
}

Tuning Guidelines

Increase num_slots (32, 64, 128): - When: Large datasets (>1 TB), many distinct ranges - Benefit: Finer-grained adaptation - Cost: More metadata, slower manifest operations

Increase k_global (8, 16): - When: Write-heavy workloads, low read QPS - Benefit: Lower WA for cold slots - Cost: Higher RA for cold reads

Increase heat_alpha (0.2, 0.3): - When: Rapidly changing workloads - Benefit: Faster adaptation to new patterns - Cost: Less stable (more thrashing)

Increase compaction_epsilon (0.15, 0.20): - When: Non-stationary workloads, multi-tenant - Benefit: Better exploration of new strategies - Cost: More suboptimal compactions (higher WA during exploration)

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Observability and Monitoring

Key Metrics

Heat Scores (per slot):

heat_score[slot_id]: f32  // Range: [0.0, 1.0]

Interpretation: - 0.0 - 0.2: Cold (rarely accessed) - 0.2 - 0.5: Warm (occasional access) - 0.5 - 0.8: Hot (frequent access) - 0.8 - 1.0: Very hot (constant access)

K-Max Values (per slot):

k_max[slot_id]: usize  // Range: [1, k_global]

Interpretation: - k=1: Leveled (hot slot) - k>1: Tiered (cold slot) - k=k_global: Fully tiered (very cold)

Bandit Metrics:

BanditSelection {
    slot_id: u32,           // Which slot was selected
    explored: bool,         // true = exploration, false = exploitation
    ucb_score: f64,         // UCB score
    avg_reward: f64,        // Historical reward
    selection_count: u64,   // Selection frequency
}

BanditReward {
    slot_id: u32,           // Which slot was compacted
    reward: f64,            // Calculated reward
    bytes_written: u64,     // Write amplification cost
    heat_score: f32,        // Access frequency weight
}

Dashboard Queries:

-- Hot slots (candidates for leveling)
SELECT slot_id, heat_score, k_max
FROM lsm_stats
WHERE heat_score > 0.8
ORDER BY heat_score DESC;

-- Compaction frequency by slot
SELECT slot_id, COUNT(*) as compactions
FROM bandit_selection
WHERE timestamp > NOW() - INTERVAL '1 hour'
GROUP BY slot_id
ORDER BY compactions DESC;

-- Reward trends (should stabilize over time)
SELECT slot_id, AVG(reward) as avg_reward, STDDEV(reward) as reward_variance
FROM bandit_reward
GROUP BY slot_id;

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Implementation Notes

Guard Key Selection

Problem: How to choose initial guard keys?

Strategy 1: Uniform Split (current implementation)

// Split key space into equal-sized ranges
guard_keys = [
    vec![0x00],              // Slot 0: [0x00, 0x10)
    vec![0x10],              // Slot 1: [0x10, 0x20)
    vec![0x20],              // Slot 2: [0x20, 0x30)
    ...
    vec![0xF0],              // Slot 15: [0xF0, ∞)
]

Strategy 2: Data-Driven Split (future work)

// Sample existing data, split by size
// Goal: Each slot contains ~equal bytes

Trade-off: - Uniform: Simple, predictable, but may create imbalanced slots - Data-driven: Balanced, but requires sampling (expensive on startup)

Compaction Triggering

L0 Flush Trigger:

if l0_files >= l0.max_files {
    // Hard stall: Reject writes
    return Err(Error::SystemPressure);
} else if l0_files >= l0.soft_throttle_threshold {
    // Soft throttle: Apply backpressure
    delay = l0.soft_throttle_base_delay_ms * (l0_files - threshold);
    sleep(delay);
}

Slot Compaction Trigger:

for slot in slots {
    if slot.runs.len() > slot.k_max {
        // Trigger slot-local tiering compaction
        scheduler.schedule_compaction(slot.slot_id);
    }
}

Bandit Selection:

// Called periodically (e.g., every 10 L0 flushes)
fn select_slot_for_compaction() -> u32 {
    if random() < epsilon {
        random_slot()  // Exploration
    } else {
        argmax(slot.ucb_score)  // Exploitation
    }
}

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Future Directions

1. Dynamic Guard Key Adjustment

Problem: Fixed guard keys may become imbalanced over time

Proposed Solution: Periodically re-partition based on slot sizes

// Every 1M writes, rebalance slots:
if write_count % 1_000_000 == 0 {
    adjust_guard_keys_to_balance_sizes();
}

Challenges: Requires moving data across slots (expensive)

2. Multi-Dimensional Heat Tracking

Current: Single heat score (access frequency)

Proposed: Multiple dimensions

pub struct HeatMetrics {
    pub read_heat: f32,   // Read frequency
    pub write_heat: f32,  // Write frequency
    pub scan_heat: f32,   // Range scan frequency
}

Benefit: Optimize for read-heavy vs write-heavy vs scan-heavy per slot

3. Contextual Bandit Scheduler

Current: Multi-armed bandit (no context)

Proposed: Use system state as context

// Context: L0 count, slot size, recent query latency
reward = f(context, action)

Benefit: Better adaptation to system pressure and query patterns

4. Learned Guard Keys

Current: Manual uniform split

Proposed: ML-based key space partitioning

// Learn guard keys that minimize cross-slot queries
guard_keys = learn_optimal_splits(query_log);

Benefit: Reduce read amplification by aligning slots with query patterns

---

Summary

ATLL (Adaptive Tiered-Leveled LSM) achieves near-Pareto-optimal trade-offs for heterogeneous workloads by:

1. Range partitioning key space into slots with fixed guard keys
2. Dynamic K-way fanout per slot based on EWMA heat tracking
3. Bandit-based scheduler for adaptive compaction decisions
4. Slot-local optimization on the RUM Pareto frontier

Result: - Hot ranges → Leveled (K=1, fast reads, low RA) - Cold ranges → Tiered (K>1, fast writes, low WA) - Overall: 8-20x WA, 5-12x RA, 1.1-1.3x SA

Comparison: - Better than Leveled: 2-5x lower WA, comparable RA for hot data - Better than Tiered: 2x lower RA for hot data, comparable WA - Better than Universal: Simpler, more predictable, better read performance

When to use ATLL: - Zipfian/skewed access patterns (80/20 rule) - Time-series with recent-heavy reads - Multi-tenant with mixed activity - General-purpose key-value workloads

When to avoid ATLL: - Uniform access patterns (no hot/cold distinction) - Pure scan workloads (sequential only) - Tiny datasets (<100 MB, overhead not worth it)

Next steps: Read Write Path and Read Path to understand how ATLL works in practice.

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Last Updated: 2025-10-31 References: Dayan et al. (Monkey, 2017), Hao et al. (LSM-Bush, 2019), Athanassoulis et al. (RUM, 2016)