[PPT] - 15-721 DATABASE SYSTEMS Lecture #07 Latch-free OLTP Indexes PowerPoint Presentation

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Andy Pavlo / / Carnegie Mellon University / / Spring 2016

DATABASE SYSTEMS

Lecture #07 – Latch-free OLTP Indexes (Part I)

15-721

@Andy_Pavlo // Carnegie Mellon University // Spring 2017

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CMU 15-721 (Spring 2017)

ADMINISTRIVIA

Peloton master branch has been updated to provide cleaner test cases.

→ There is now a separate file for Skip List tests. → Your implementation should match the behavior of the Bw-Tree.

We will be sending out information on how to access the MemSQL development machines.

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TODAY’S AGENDA

T-Trees Skip Lists Index Implementation Issues

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T-TREES

Based on AVL Trees. Instead of storing keys in nodes, store pointers to their original values. Proposed in 1986 from Univ. of Wisconsin Used in TimesTen and other early in-memory DBMSs during the 1990s.

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A STUDY OF INDEX STRUCTURES FOR MAIN MEMORY DATABASE MANAGEMENT SYSTEMS VLDB 1986

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T-Tree Node

T-TREES

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Min-K

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Parent Pointer Right Child Pointer Left Child Pointer

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T-Tree Node

T-TREES

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Min-K

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Parent Pointer Right Child Pointer Left Child Pointer

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Data Pointers

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T-Tree Node

T-TREES

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Min-K

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Parent Pointer Right Child Pointer Left Child Pointer

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Node Boundaries

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Key Space (Low→High) T-Tree Node

T-TREES

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Min-K

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Parent Pointer Right Child Pointer Left Child Pointer

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1 2 3 4 5 6 7

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Key Space (Low→High) T-Tree Node

T-TREES

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Min-K

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Parent Pointer Right Child Pointer Left Child Pointer

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1 2 3 4 5 6 7 1 2 3 4 5 6 7

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Key Space (Low→High) T-Tree Node

T-TREES

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Min-K

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Parent Pointer Right Child Pointer Left Child Pointer

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1 2 3 4 5 6 7 1 2 3 4 5 6 7

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T-TREES

Advantages

→ Uses less memory because it does not store keys inside of each node. → Inner nodes contain key/value pairs (like B-Tree).

Disadvantages

→ Difficult to rebalance. → Difficult to implement safe concurrent access. → Have to chase pointers when scanning range or performing binary search inside of a node.

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OBSERVATION

The easiest way to implement a dynamic order- preserving index is to use a sorted linked list. All operations have to linear search.

→ Average Cost: O(N)

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K1 K2 K3 K4 K6 K5 K7

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OBSERVATION

The easiest way to implement a dynamic order- preserving index is to use a sorted linked list. All operations have to linear search.

→ Average Cost: O(N)

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K1 K2 K3 K4 K6 K5 K7

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OBSERVATION

The easiest way to implement a dynamic order- preserving index is to use a sorted linked list. All operations have to linear search.

→ Average Cost: O(N)

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K1 K2 K3 K4 K6 K5 K7

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SKIP LISTS

Multiple levels of linked lists with extra pointers that skip over intermediate nodes. Maintains keys in sorted order without requiring global rebalancing.

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SKIP LISTS: A PROBABILISTIC ALTERNATIVE TO BALANCED TREES CACM Volume 33 Issue 6 1990

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SKIP LISTS

A collection of lists at different levels

→ Lowest level is a sorted, singly linked list of all keys → 2nd level links every other key → 3rd level links every fourth key → In general, a level has half the keys of one below it

To insert a new key, flip a coin to decide how many levels to add the new key into. Provides approximate O(log n) search times.

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End Levels

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K6 V6

SKIP LISTS: EXAMPLE

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∞ ∞ ∞

P=N P=N/2 P=N/4

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End Levels

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K6 V6

SKIP LISTS: EXAMPLE

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∞ ∞ ∞

P=N P=N/2 P=N/4

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End Levels

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K6 V6

SKIP LISTS: EXAMPLE

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∞ ∞ ∞

P=N P=N/2 P=N/4

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End Levels

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K6 V6

SKIP LISTS: EXAMPLE

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∞ ∞ ∞

P=N P=N/2 P=N/4

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End Levels

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K6 V6

SKIP LISTS: INSERT

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P=N P=N/2 P=N/4

Insert K5

K5 V5 K5 K5

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K5 V5 K5 K5 K6 V6

Levels

SKIP LISTS: SEARCH

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∞ ∞ ∞

P=N P=N/2 P=N/4

Find K3

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K5 V5 K5 K5 K6 V6

Levels

SKIP LISTS: SEARCH

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∞ ∞ ∞

P=N P=N/2 P=N/4

Find K3

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SKIP LISTS: ADVANTAGES

Uses less memory than a typical B+tree (only if you don’t include reverse pointers). Insertions and deletions do not require rebalancing. It is possible to implement a concurrent skip list using only CAS instructions.

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CONCURRENT SKIP LIST

Can implement insert and delete without locks using only CAS operations.

→ Only support linking in one direction

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CONCURRENT MAINTENANCE OF SKIP LISTS

Univ. of Maryland Tech Report 1990

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End Levels

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K6 V6

SKIP LISTS: INSERT

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P=N P=N/2 P=N/4

Insert K5

K5 K5 K5 V5

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SKIP LISTS: DELETE

First logically remove a key from the index by setting a flag to tell threads to ignore. Then physically remove the key once we know that no other thread is holding the reference.

→ Perform CaS to update the predecessor’s pointer.

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Source: Stephen Tu

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K5 V5 K5 K5 K6 V6

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SKIP LISTS: DELETE

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∞ ∞ ∞

P=N P=N/2 P=N/4

Delete K5

Del

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Del

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Del

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Del

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K5 V5 K5 K5 K6 V6

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SKIP LISTS: DELETE

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∞ ∞ ∞

P=N P=N/2 P=N/4

Delete K5

Del

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Del

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Del

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Del

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Del

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Del

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K5 V5 K5 K5 K6 V6

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SKIP LISTS: DELETE

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∞ ∞ ∞

P=N P=N/2 P=N/4

Delete K5

Del

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Del

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Del

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Del

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Del

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Del

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Del

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K5 V5 K5 K5 K6 V6

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SKIP LISTS: DELETE

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∞ ∞ ∞

P=N P=N/2 P=N/4

Delete K5

Del

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Del

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Del

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Del

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Del

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Del

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K5 V5 K5 K5 K6 V6

Levels

SKIP LISTS: DELETE

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∞ ∞ ∞

P=N P=N/2 P=N/4

Delete K5

Del

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Del

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Del

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Del

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Del

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Del

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K5 V5 K5 K5 K6 V6

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SKIP LISTS: DELETE

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∞ ∞ ∞

P=N P=N/2 P=N/4

Delete K5

Del

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Del

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Del

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Del

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Del

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Del

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Del

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K6 V6

Levels

SKIP LISTS: DELETE

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∞ ∞ ∞

P=N P=N/2 P=N/4

Delete K5

Del

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Del

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Del

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Del

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CONCURRENT SKIP LIST

Be careful about how you order operations. If the DBMS invokes operation on the index, it can never “fail”

→ A txn can only abort due to higher-level conflicts. → If a CaS fails, then the index will retry until it succeeds.

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SKIP LISTS: DISADVANTAGES

Invoking random number generator multiple times per insert is slow. Not cache friendly because they do not optimize locality of references. Reverse search is non-trivial.

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SKIP LIST OPTIMIZATIONS

Reducing RAND() invocations. Packing multiple keys in a node. Reverse iteration with a stack. Reusing nodes with memory pools.

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SKIP LISTS: DONE RIGHT Ticki(?) Blog 2016

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SKIP LIST: COMBINE NODES

Store multiple keys in a single node.

→ Insert Key: Find the node where it should go and look for a free slot. Perform CaS to store new key. If no slot is available, insert new node. → Search Key: Perform linear search on keys in each node.

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K2 V2 K3 V3 K6 V6

Source: Ticki

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SKIP LIST: COMBINE NODES

Store multiple keys in a single node.

→ Insert Key: Find the node where it should go and look for a free slot. Perform CaS to store new key. If no slot is available, insert new node. → Search Key: Perform linear search on keys in each node.

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K2 V2 K3 V3 K6 V6

Source: Ticki

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SKIP LIST: COMBINE NODES

Store multiple keys in a single node.

→ Insert Key: Find the node where it should go and look for a free slot. Perform CaS to store new key. If no slot is available, insert new node. → Search Key: Perform linear search on keys in each node.

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K2 V2 K3 V3 K6 V6

Insert K4

Source: Ticki

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SKIP LIST: COMBINE NODES

Store multiple keys in a single node.

→ Insert Key: Find the node where it should go and look for a free slot. Perform CaS to store new key. If no slot is available, insert new node. → Search Key: Perform linear search on keys in each node.

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K2 V2 K3 V3 K6 V6

K4

V4

Insert K4

Source: Ticki

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SKIP LIST: COMBINE NODES

Store multiple keys in a single node.

→ Insert Key: Find the node where it should go and look for a free slot. Perform CaS to store new key. If no slot is available, insert new node. → Search Key: Perform linear search on keys in each node.

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K2 V2 K3 V3 K6 V6

K4

V4

Search K6

Source: Ticki

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End

K1 V1 K2 K2 V2 K3 V3 K4 V4 K4 K5 V5 K5 K5 K6 V6

Levels

SKIP LISTS: REVERSE SEARCH

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∞ ∞ ∞

P=N P=N/2 P=N/4

Find [K4,K2]

K2<K5 K2=K2

Stack: K2 K4 K3

K2<K4

Source: Mark Papadakis

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INDEX IMPLEMENTATION ISSUES

Memory Pools Garbage Collection Non-Unique Keys Variable-length Keys

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MEMORY POOLS

We don’t want to be calling malloc and free anytime we need to add or delete a node. If all the nodes are the same size, then the index can maintain a pool of available nodes.

→ Insert: Grab a free node, otherwise create a new one. → Delete: Add the node back to the free pool.

Need some policy to decide when to retract the pool size.

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GARBAGE COLLECTION

We need to know when it is safe to reclaim memory for deleted nodes in a latch-free index.

→ Reference Counting → Epoch-based Reclamation → Hazard Pointers → Many others…

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K2 V2 K3 V3 K4 V4

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GARBAGE COLLECTION

We need to know when it is safe to reclaim memory for deleted nodes in a latch-free index.

→ Reference Counting → Epoch-based Reclamation → Hazard Pointers → Many others…

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K2 V2 K3 V3 K4 V4

X

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GARBAGE COLLECTION

We need to know when it is safe to reclaim memory for deleted nodes in a latch-free index.

→ Reference Counting → Epoch-based Reclamation → Hazard Pointers → Many others…

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K2 V2 K4 V4

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GARBAGE COLLECTION

We need to know when it is safe to reclaim memory for deleted nodes in a latch-free index.

→ Reference Counting → Epoch-based Reclamation → Hazard Pointers → Many others…

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K2 V2 K4 V4

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REFERENCE COUNTING

Maintain a counter for each node to keep track of the number of threads that are accessing it.

→ Increment the counter before accessing. → Decrement it when finished. → A node is only safe to delete when the count is zero.

This has bad performance for multi-core CPUs

→ Incrementing/decrementing counters causes a lot of cache coherence traffic.

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OBSERVATION

We don’t actually care about the actual value of the reference counter. We only need to know when it reaches zero. We don’t have to perform garbage collection immediately when the counter reaches zero.

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Source: Stephen Tu

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EPOCH GARBAGE COLLECTION

Maintain a global epoch counter that is periodically updated (e.g., every 10 ms).

→ Keep track of what threads enter the index during an epoch and when they leave.

Mark the current epoch of a node when it is marked for deletion.

→ The node can be reclaimed once all threads have left that epoch (and all preceding epochs).

Also known as Read-Copy-Update (RCU) in Linux.

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NON-UNIQUE INDEXES

Approach #1: Duplicate Keys

→ Use the same node layout but store duplicate keys multiple times.

Approach #2: Value Lists

→ Store each key only once and maintain a linked list of unique values.

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B+Tree Leaf Node

DUPLICATE KEYS

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Sorted Keys K1 K1 K1 K2 K2 • • • Kn

¤

Next # Level # Slots Values

¤ ¤ ¤ ¤ ¤ • • • ¤

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B+Tree Leaf Node

VALUE LISTS

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Values

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• •

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Next # Level # Slots Sorted Keys K1 K2 K3 K4 K5 • • • Kn

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VARIABLE LENGTH KEYS

Approach #1: Pointers

→ Store the keys as pointers to the tuple’s attribute.

Approach #2: Variable Length Nodes

→ The size of each node in the index can vary. → Requires careful memory management.

Approach #3: Padding

→ Always pad the key to be max length of the key type.

Approach #4: Key Map

→ Embed an array of pointers that map to the key + value list within the node.

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B+Tree Leaf Node

KEY MAP

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Key+Values

• •

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Next # Level # Slots Key Map K1 V1 V2

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K2 V1 V2 V3

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PARTING THOUGHTS

Managing a concurrent index looks a lot like managing a database. Skip List is really easy to implement. Concurrent Skip List is more tricky. Epoch garbage collection is more cache friendly.

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NEXT CLASS

More OLTP Indexes

→ Microsoft Bw-Tree → HyPer ART

Crash course on performance testing.

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