Slot Routing

How keys are mapped to slots using binary search on guard keys. Range queries and slot overlap detection.

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Overview

Slot routing maps keys to slots (range shards) using fixed guard keys. This enables: - Per-range adaptation: Each slot chooses its own compaction strategy (K-max) - Parallel compaction: Compact multiple slots concurrently - Efficient range queries: Scan only slots overlapping [start, end)

Key properties: - Deterministic: Same key always maps to same slot - Fast: Binary search O(log num_slots) = ~4 hops for 16 slots - Stable: Guard keys never change (unless manual rebalancing) - Range-preserving: Adjacent keys often in same slot (locality)

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Guard Key Structure

Slots are defined by [guard_key_min, guard_key_max) boundaries:

Slot 0:  [0x00, 0x40)  ← Handles keys 0x00..=0x3F
Slot 1:  [0x40, 0x80)  ← Handles keys 0x40..=0x7F
Slot 2:  [0x80, 0xC0)  ← Handles keys 0x80..=0xBF
Slot 3:  [0xC0, ∞)     ← Handles keys 0xC0..=0xFF

Invariants: 1. No gaps: Every key falls into exactly one slot 2. No overlaps: slot[i].max = slot[i+1].min 3. Sorted: slot[i].min < slot[i+1].min for all i

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Point Query Routing

Binary Search Algorithm

pub fn find_slot_for_key(&self, key: &[u8]) -> u32 {
    let mut left = 0;
    let mut right = self.slots.len();

    while left < right {
        let mid = (left + right) / 2;
        let slot = &self.slots[mid];

        if key < slot.guard_key_min.as_slice() {
            right = mid;
        } else if key >= slot.guard_key_max.as_slice() {
            left = mid + 1;
        } else {
            // Found: slot.min <= key < slot.max
            return mid as u32;
        }
    }

    panic!("No slot found for key (guard key invariant violated)");
}

Time complexity: O(log n) where n = number of slots

Example (16 slots, searching for key = 0x75):

Iteration 1: left=0, right=16, mid=8
  Slot 8: [0x80, 0x90)
  0x75 < 0x80 → right=8

Iteration 2: left=0, right=8, mid=4
  Slot 4: [0x40, 0x50)
  0x75 >= 0x50 → left=5

Iteration 3: left=5, right=8, mid=6
  Slot 6: [0x60, 0x70)
  0x75 >= 0x70 → left=7

Iteration 4: left=7, right=8, mid=7
  Slot 7: [0x70, 0x80)
  0x70 <= 0x75 < 0x80 → Found!

Result: Slot 7 (4 iterations)

Comparison to Alternatives

Routing Strategy	Time Complexity	Pros	Cons
Binary search	O(log n)	Fast, simple, range-preserving	Requires sorted guards
Hash table	O(1)	Fastest point queries	No range queries, no locality
Linear scan	O(n)	Simple	Too slow (n iterations)
Trie	O(k) k=key length	Prefix compression	Complex, high memory

Binary search wins: Balance of speed, simplicity, and range query support.

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Range Query Routing

Range queries scan multiple slots:

Find Overlapping Slots

pub fn find_slots_for_range(&self, start: &[u8], end: &[u8]) -> Vec<u32> {
    // 1. Find first slot containing start
    let start_slot = self.find_slot_for_key(start);

    // 2. Find last slot containing end
    let end_slot = self.find_slot_for_key(end);

    // 3. Return all slots in range [start_slot, end_slot]
    (start_slot..=end_slot).collect()
}

Example (range query ["user:1000", "user:9999"]):

Guard keys (16 slots, uniform split):
  Slot 0: [0x00, 0x10)
  Slot 1: [0x10, 0x20)
  ...
  Slot 7: [0x70, 0x80)  ← "user:1000" (0x75...) falls here
  Slot 8: [0x80, 0x90)
  ...
  Slot 11: [0xB0, 0xC0) ← "user:9999" (0x75...) falls here (same slot!)

Result: Only scan Slot 7 (start and end in same slot)

Range Scan Implementation

pub async fn scan(&self, start: &[u8], end: &[u8]) -> Result<Vec<(Vec<u8>, Vec<u8>)>> {
    let slots = self.find_slots_for_range(start, end);
    let mut results = Vec::new();

    for slot_id in slots {
        let slot = &self.slots[slot_id as usize];

        // Scan all runs in this slot
        for run in &slot.runs {
            // 1. Check bloom filter (skip if key range doesn't overlap)
            if !run.bloom.may_contain_range(start, end) {
                continue;
            }

            // 2. Scan SSTable
            let mut iter = run.sstable.range(start, end).await?;
            while let Some((key, value)) = iter.next().await? {
                results.push((key, value));
            }
        }
    }

    // 3. Merge results (keys may be duplicated across runs)
    results.sort_by(|a, b| a.0.cmp(&b.0));
    results.dedup_by(|a, b| a.0 == b.0);  // Keep latest version

    Ok(results)
}

Optimization: Bloom filter range check skips SSTables that definitely don't contain keys in [start, end).

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Guard Key Selection Strategies

Uniform Split (Default)

Divide key space evenly:

pub fn uniform_guard_keys(num_slots: u32) -> Vec<Vec<u8>> {
    let mut guards = vec![];
    let step = 256 / num_slots;

    for i in 0..num_slots {
        guards.push(vec![(i * step) as u8]);
    }

    guards.push(vec![0xFF]);  // Final boundary
    guards
}

Example (4 slots):

Step = 256 / 4 = 64
Slot 0: [0x00, 0x40)
Slot 1: [0x40, 0x80)
Slot 2: [0x80, 0xC0)
Slot 3: [0xC0, 0xFF]

Pros: - Simple, predictable - No sampling required - Works for any workload

Cons: - Assumes uniform key distribution - Skewed workloads create imbalanced slots

Data-Driven Split (Future)

Sample existing keys, split by percentiles:

pub async fn data_driven_guard_keys(num_slots: u32) -> Vec<Vec<u8>> {
    // 1. Sample 10K random keys from L0 and slots
    let samples = self.sample_keys(10_000).await?;

    // 2. Sort samples
    samples.sort();

    // 3. Choose percentile boundaries
    let mut guards = vec![];
    for i in 0..num_slots {
        let percentile = (i as f64) / (num_slots as f64);
        let idx = (percentile * samples.len() as f64) as usize;
        guards.push(samples[idx].clone());
    }

    guards
}

Pros: - Balanced slot sizes - Adapts to actual key distribution

Cons: - Requires sampling (slow) - Changes over time (not stable)

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Slot Metadata

Each slot tracks its own state:

pub struct Slot {
    /// Slot ID (0-indexed)
    pub slot_id: u32,

    /// Inclusive lower bound
    pub guard_key_min: Vec<u8>,

    /// Exclusive upper bound
    pub guard_key_max: Vec<u8>,

    /// Sorted runs in this slot (K-way fanout)
    pub runs: Vec<SortedRun>,

    /// Maximum K allowed (adaptive based on heat)
    pub k_max: usize,

    /// Heat score (EWMA of access frequency)
    pub heat_score: f32,

    /// Total size of all runs (bytes)
    pub total_size: u64,

    /// Entry count (approximate)
    pub entry_count: u64,
}

Example (Slot 1 in a hot workload):

Slot {
    slot_id: 1,
    guard_key_min: vec![0x40],
    guard_key_max: vec![0x80],
    runs: vec![
        SortedRun { id: 42, size: 128 MB, entries: 1M },
    ],
    k_max: 1,  // Leveled (hot slot)
    heat_score: 0.85,
    total_size: 134_217_728,
    entry_count: 1_048_576,
}

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Parallel Compaction

Slots enable parallel compaction:

pub async fn compact_parallel(&mut self) -> Result<()> {
    // 1. Select N slots via bandit scheduler
    let selected_slots = self.scheduler.select_slots(num_workers: 4);

    // 2. Spawn compaction tasks
    let tasks: Vec<_> = selected_slots.iter().map(|slot_id| {
        let slot = self.slots[*slot_id as usize].clone();
        tokio::spawn(async move {
            compact_slot(slot).await
        })
    }).collect();

    // 3. Await all tasks
    for task in tasks {
        task.await??;
    }

    Ok(())
}

Benefit: 4x throughput (compact 4 slots in parallel on 4-core CPU).

Synchronization: Each slot has its own lock, no contention between slots.

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Performance Characteristics

Routing Latency

Benchmark (16 slots):

Operation              Latency (p50)   Latency (p95)
────────────────────────────────────────────────────
find_slot_for_key      40ns            60ns
find_slots_for_range   80ns            120ns

Breakdown (find_slot_for_key): - Binary search: 4 iterations × 8ns/iteration = 32ns - Guard key comparison: 8ns - Total: ~40ns

Routing Throughput

25M lookups/sec on single thread (40ns per lookup).

Comparison to hash routing: - Hash routing: 20ns (faster, but no range queries) - Binary search: 40ns (2x slower, but supports ranges)

Trade-off: Accept 2x slower point queries for range query support.

Range Query Performance

Benchmark (scan 10K keys across 3 slots):

Phase                  Time      Percentage
─────────────────────────────────────────────
Find overlapping slots 80ns      <0.01%
Bloom filter checks    300ns     0.02%
SSTable range scans    1.2ms     99.98%
Merge and dedup        5ms       <0.01%
─────────────────────────────────────────────
Total                  6.5ms     100%

Key insight: Routing overhead is negligible (<0.01%), SSTable I/O dominates.

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Edge Cases

1. Key Exactly at Boundary

Scenario: Key equals guard_key_max of slot.

// Slot 0: [0x00, 0x40)
// Slot 1: [0x40, 0x80)

find_slot_for_key(&[0x40])  // Which slot?

Answer: Slot 1 (boundaries are [inclusive, exclusive))

Invariant: slot.min <= key < slot.max

2. Empty Range Query

Scenario: start > end (invalid range).

find_slots_for_range(&[0x80], &[0x40])  // start > end

Handling:

pub fn find_slots_for_range(&self, start: &[u8], end: &[u8]) -> Vec<u32> {
    if start >= end {
        return vec![];  // Empty range, no slots
    }

    // Normal logic
}

3. Single-Byte Keys vs Multi-Byte Keys

Scenario: Mix of short and long keys.

// Short key
find_slot_for_key(&[0x75])  → Slot 7

// Long key (same prefix)
find_slot_for_key(&[0x75, 0x01, 0x02, 0x03])  → Slot 7 (same slot!)

Comparison: Lexicographic byte-by-byte.

0x75 vs 0x70: 0x75 > 0x70 → Continue
0x75 vs 0x80: 0x75 < 0x80 → In range [0x70, 0x80)

0x75 0x01 0x02 0x03 vs 0x70: First byte 0x75 > 0x70 → Continue
0x75 0x01 0x02 0x03 vs 0x80: First byte 0x75 < 0x80 → In range

Locality: Keys with same prefix often in same slot (good for range queries).

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Code Example: Complete Routing Implementation

pub struct SlotRouter {
    slots: Vec<Slot>,
}

impl SlotRouter {
    pub fn new(num_slots: u32) -> Self {
        let guard_keys = Self::uniform_guard_keys(num_slots);
        let mut slots = Vec::new();

        for i in 0..num_slots as usize {
            slots.push(Slot {
                slot_id: i as u32,
                guard_key_min: guard_keys[i].clone(),
                guard_key_max: guard_keys[i + 1].clone(),
                runs: vec![],
                k_max: 4,  // Default K_global
                heat_score: 0.0,
                total_size: 0,
                entry_count: 0,
            });
        }

        Self { slots }
    }

    pub fn find_slot_for_key(&self, key: &[u8]) -> u32 {
        self.slots
            .binary_search_by(|slot| {
                if key < slot.guard_key_min.as_slice() {
                    std::cmp::Ordering::Greater
                } else if key >= slot.guard_key_max.as_slice() {
                    std::cmp::Ordering::Less
                } else {
                    std::cmp::Ordering::Equal
                }
            })
            .unwrap() as u32
    }

    pub fn find_slots_for_range(&self, start: &[u8], end: &[u8]) -> Vec<u32> {
        if start >= end {
            return vec![];
        }

        let start_slot = self.find_slot_for_key(start);
        let end_slot = self.find_slot_for_key(end);

        (start_slot..=end_slot).collect()
    }

    fn uniform_guard_keys(num_slots: u32) -> Vec<Vec<u8>> {
        let mut guards = vec![];
        let step = 256 / num_slots;

        for i in 0..num_slots {
            guards.push(vec![(i * step) as u8]);
        }

        guards.push(vec![0xFF]);
        guards
    }
}

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Summary

Slot routing maps keys to range-partitioned slots:

1. Binary search - O(log n) routing, 40ns latency for 16 slots
2. Guard keys - Fixed boundaries, stable, predictable
3. Range queries - Scan contiguous slots, skip non-overlapping
4. Parallel compaction - Independent per-slot locks, no contention

Performance: - Point query routing: 40ns - Range query routing: 80ns - Throughput: 25M lookups/sec

Next: Compaction Lifecycle - The most complex subsystem

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Last Updated: 2025-10-31 See Also: ATLL Architecture, Guard-Based Partitioning