View
4
Download
0
Category
Preview:
Citation preview
Andy Pavlo // Carnegie Mellon University // Spring 2016
Lecture #07 – Indexing (OLTP)
DATABASE SYSTEMS
15-721
CMU 15-721 (Spring 2016)
TODAY ’S AGENDA
Latch Implementations Modern OLTP Indexes
2
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
__sync_bool_compare_and_swap(&M, 20, 30)
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
__sync_bool_compare_and_swap(&M, 20, 30)
Address
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
M __sync_bool_compare_and_swap(&M, 20, 30) 20
Address
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
M __sync_bool_compare_and_swap(&M, 20, 30) 20
Compare Value
Address
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
M __sync_bool_compare_and_swap(&M, 20, 30) 20
Compare Value
Address New
Value
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
M __sync_bool_compare_and_swap(&M, 20, 30) 20
Compare Value
Address New
Value
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
M __sync_bool_compare_and_swap(&M, 20, 30) 30
Compare Value
Address New
Value
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
M __sync_bool_compare_and_swap(&M, 20, 30) 30 25 35
Compare Value
Address New
Value
CMU 15-721 (Spring 2016)
COMPARE-AND-SWAP
Atomic instruction that compares contents of a memory location M to a given value V → If values are equal, installs new given value V’ in M → Otherwise operation fails
3
M __sync_bool_compare_and_swap(&M, 20, 30) 30 X 25 35
Compare Value
Address New
Value
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Blocking OS Mutex Test-and-Set Spinlock Queue-based Spinlock Reader-Writer Locks
4
Source: Anastasia Ailamaki
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #1: Blocking OS Mutex → Simple to use → Non-scalable (about 25ns per lock/unlock invocation) → Example: pthread_mutex_t (calls futex)
5
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #1: Blocking OS Mutex → Simple to use → Non-scalable (about 25ns per lock/unlock invocation) → Example: pthread_mutex_t (calls futex)
5
pthread_mutex_t lock; ⋮ pthread_mutex_lock(&lock); // Do something special... pthread_mutex_unlock(&lock);
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #1: Blocking OS Mutex → Simple to use → Non-scalable (about 25ns per lock/unlock invocation) → Example: pthread_mutex_t (calls futex)
5
pthread_mutex_t lock; ⋮ pthread_mutex_lock(&lock); // Do something special... pthread_mutex_unlock(&lock);
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #1: Blocking OS Mutex → Simple to use → Non-scalable (about 25ns per lock/unlock invocation) → Example: pthread_mutex_t (calls futex)
5
pthread_mutex_t lock; ⋮ pthread_mutex_lock(&lock); // Do something special... pthread_mutex_unlock(&lock);
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #2: Test-and-Set Spinlock (TAS) → Very efficient (single instruction to lock/unlock) → Non-scalable, not cache friendly → Example: std::atomic_flag
6
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #2: Test-and-Set Spinlock (TAS) → Very efficient (single instruction to lock/unlock) → Non-scalable, not cache friendly → Example: std::atomic_flag
6
std::atomic_flag lock; ⋮ while (lock.test_and_set(…)) { // Yield? Abort? Retry? }
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #2: Test-and-Set Spinlock (TAS) → Very efficient (single instruction to lock/unlock) → Non-scalable, not cache friendly → Example: std::atomic_flag
6
std::atomic_flag lock; ⋮ while (lock.test_and_set(…)) { // Yield? Abort? Retry? }
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #2: Test-and-Set Spinlock (TAS) → Very efficient (single instruction to lock/unlock) → Non-scalable, not cache friendly → Example: std::atomic_flag
6
std::atomic_flag lock; ⋮ while (lock.test_and_set(…)) { // Yield? Abort? Retry? }
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #3: Queue-based Spinlock (MCS) → More efficient than mutex, better cache locality → Non-trivial memory management → Example: std::atomic_flag
7
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #3: Queue-based Spinlock (MCS) → More efficient than mutex, better cache locality → Non-trivial memory management → Example: std::atomic_flag
7
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #3: Queue-based Spinlock (MCS) → More efficient than mutex, better cache locality → Non-trivial memory management → Example: std::atomic_flag
7
next
Base Lock
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #3: Queue-based Spinlock (MCS) → More efficient than mutex, better cache locality → Non-trivial memory management → Example: std::atomic_flag
7
next
Base Lock
CPU1
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #3: Queue-based Spinlock (MCS) → More efficient than mutex, better cache locality → Non-trivial memory management → Example: std::atomic_flag
7
next
Base Lock
next
CPU1 Lock
CPU1
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #3: Queue-based Spinlock (MCS) → More efficient than mutex, better cache locality → Non-trivial memory management → Example: std::atomic_flag
7
next
Base Lock
next
CPU1 Lock
CPU1 CPU2
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #3: Queue-based Spinlock (MCS) → More efficient than mutex, better cache locality → Non-trivial memory management → Example: std::atomic_flag
7
next
Base Lock
next
CPU1 Lock
CPU1 CPU2
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #3: Queue-based Spinlock (MCS) → More efficient than mutex, better cache locality → Non-trivial memory management → Example: std::atomic_flag
7
next
Base Lock
next
CPU1 Lock
next
CPU2 Lock
CPU1 CPU2
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #3: Queue-based Spinlock (MCS) → More efficient than mutex, better cache locality → Non-trivial memory management → Example: std::atomic_flag
7
next
Base Lock
next
CPU1 Lock
next
CPU2 Lock
CPU1 CPU2 CPU3
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
=1
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
=1
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
=1 =2
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
=1 =2
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
=1 =2 =1
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
=1 =2 =1
CMU 15-721 (Spring 2016)
LATCH IMPLEMENTATIONS
Choice #4: Reader-Writer Locks → Allows for concurrent readers → Have to manage read/write queues to avoid starvation → Can be implemented on top of spinlocks
8
read write
Latch
=0 =0
=0 =0
=1 =2 =1 =1
CMU 15-721 (Spring 2016)
MODERN INDEXES
Bw-Tree (Hekaton) Concurrent Skip Lists (MemSQL) ART Index (HyPer)
9
CMU 15-721 (Spring 2016)
BW-TREE
Latch-free B+Tree index → Threads never need to set latches or block.
Key Idea #1: Deltas → No updates in place → Reduces cache invalidation.
Key Idea #2: Mapping Table → Allows for CAS of physical locations of pages.
10
THE BW-TREE: A B-TREE FOR NEW HARDWARE ICDE 2013
CMU 15-721 (Spring 2016)
BW-TREE: MAPPING TABLE
11
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
Index Page
CMU 15-721 (Spring 2016)
BW-TREE: MAPPING TABLE
11
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
Index Page
102
101
104
CMU 15-721 (Spring 2016)
BW-TREE: MAPPING TABLE
11
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
Index Page
102
101
104
CMU 15-721 (Spring 2016)
BW-TREE: MAPPING TABLE
11
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
Index Page
CMU 15-721 (Spring 2016)
BW-TREE: MAPPING TABLE
11
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
102 104
102 104
Index Page
CMU 15-721 (Spring 2016)
BW-TREE: DELTA UPDATES
12
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
Page 102
Source: Justin Levandoski
CMU 15-721 (Spring 2016)
BW-TREE: DELTA UPDATES
Each update to a page produces a new delta.
12
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
Page 102
Source: Justin Levandoski
CMU 15-721 (Spring 2016)
BW-TREE: DELTA UPDATES
Each update to a page produces a new delta.
12
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
Source: Justin Levandoski
CMU 15-721 (Spring 2016)
BW-TREE: DELTA UPDATES
Each update to a page produces a new delta.
12
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
Delta physically points to base page.
Source: Justin Levandoski
CMU 15-721 (Spring 2016)
BW-TREE: DELTA UPDATES
Each update to a page produces a new delta.
12
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102 Install delta address in physical address slot of mapping table using CAS.
Delta physically points to base page.
Source: Justin Levandoski
CMU 15-721 (Spring 2016)
BW-TREE: DELTA UPDATES
Each update to a page produces a new delta.
12
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102 Install delta address in physical address slot of mapping table using CAS.
Delta physically points to base page.
Source: Justin Levandoski
CMU 15-721 (Spring 2016)
BW-TREE: DELTA UPDATES
Each update to a page produces a new delta.
12
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102 Install delta address in physical address slot of mapping table using CAS.
Delta physically points to base page.
Source: Justin Levandoski
CMU 15-721 (Spring 2016)
BW-TREE: DELTA UPDATES
Each update to a page produces a new delta.
12
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
Install delta address in physical address slot of mapping table using CAS.
Delta physically points to base page.
Source: Justin Levandoski
CMU 15-721 (Spring 2016)
BW-TREE: DELTA UPDATES
Each update to a page produces a new delta.
12
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
Install delta address in physical address slot of mapping table using CAS.
Delta physically points to base page.
Source: Justin Levandoski
CMU 15-721 (Spring 2016)
BW-TREE: SEARCH
13
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
CMU 15-721 (Spring 2016)
BW-TREE: SEARCH
Traverse tree like a regular B+tree.
13
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
CMU 15-721 (Spring 2016)
BW-TREE: SEARCH
Traverse tree like a regular B+tree.
13
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
If mapping table points to delta chain, stop at first occurrence of search key.
CMU 15-721 (Spring 2016)
BW-TREE: SEARCH
Traverse tree like a regular B+tree.
13
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
Otherwise, perform binary search on base page.
If mapping table points to delta chain, stop at first occurrence of search key.
CMU 15-721 (Spring 2016)
BW-TREE: CONTENTION UPDATES
14
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
CMU 15-721 (Spring 2016)
BW-TREE: CONTENTION UPDATES
Threads may try to install updates to same state of the page.
14
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
CMU 15-721 (Spring 2016)
BW-TREE: CONTENTION UPDATES
Threads may try to install updates to same state of the page.
14
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
CMU 15-721 (Spring 2016)
BW-TREE: CONTENTION UPDATES
Threads may try to install updates to same state of the page.
14
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48 ▲Insert 16
CMU 15-721 (Spring 2016)
BW-TREE: CONTENTION UPDATES
Threads may try to install updates to same state of the page.
14
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
Winner succeeds, any losers must retry or abort
▲Insert 16
CMU 15-721 (Spring 2016)
BW-TREE: CONTENTION UPDATES
Threads may try to install updates to same state of the page.
14
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
Winner succeeds, any losers must retry or abort
▲Insert 16
CMU 15-721 (Spring 2016)
BW-TREE: CONTENTION UPDATES
Threads may try to install updates to same state of the page.
14
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
Winner succeeds, any losers must retry or abort
▲Insert 16
CMU 15-721 (Spring 2016)
BW-TREE: CONTENTION UPDATES
Threads may try to install updates to same state of the page.
14
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
Winner succeeds, any losers must retry or abort
▲Insert 16 X
CMU 15-721 (Spring 2016)
BW-TREE: DELTA TYPES
Record Update Deltas → Insert/Delete/Update of record on a page
Structure Modification Deltas → Split/Merge information
15
CMU 15-721 (Spring 2016)
BW-TREE: CONSOLIDATION
16
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
CMU 15-721 (Spring 2016)
BW-TREE: CONSOLIDATION
Consolidate updates by creating new page with deltas applied.
16
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
CMU 15-721 (Spring 2016)
BW-TREE: CONSOLIDATION
Consolidate updates by creating new page with deltas applied.
16
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
CMU 15-721 (Spring 2016)
BW-TREE: CONSOLIDATION
Consolidate updates by creating new page with deltas applied.
16
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102 ▲Insert 50
CMU 15-721 (Spring 2016)
BW-TREE: CONSOLIDATION
Consolidate updates by creating new page with deltas applied.
16
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
CMU 15-721 (Spring 2016)
BW-TREE: CONSOLIDATION
Consolidate updates by creating new page with deltas applied.
16
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
CAS-ing the mapping table address ensures no deltas are missed.
▲Insert 55
New 102
CMU 15-721 (Spring 2016)
BW-TREE: CONSOLIDATION
Consolidate updates by creating new page with deltas applied.
16
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
CAS-ing the mapping table address ensures no deltas are missed.
▲Insert 55
New 102
CMU 15-721 (Spring 2016)
BW-TREE: CONSOLIDATION
Consolidate updates by creating new page with deltas applied.
16
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
CAS-ing the mapping table address ensures no deltas are missed.
▲Insert 55
New 102
Old page + deltas are marked as garbage.
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
Operations are tagged with an epoch → Each epoch tracks the threads that are part of it and
the objects that can be reclaimed. → Thread joins an epoch prior to each operation and
post objects that can be reclaimed for the current epoch (not necessarily the one it joined)
Garbage for an epoch reclaimed only when all threads have exited the epoch.
17
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
Epoch Table
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
CPU1
Epoch Table
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
CPU1
Epoch Table
CPU1
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
CPU1
CPU2
Epoch Table
CPU1 CPU2
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
CPU1
CPU2
Epoch Table
CPU1 CPU2
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
CPU1
CPU2
Epoch Table
CPU1 CPU2
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
CPU1
Epoch Table
CPU1 CPU2
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
CPU1
Epoch Table
CPU1
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
Epoch Table
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
▲Insert 50
Page 102
▲Delete 48
▲Insert 55
New 102
Epoch Table
X
CMU 15-721 (Spring 2016)
BW-TREE: GARBAGE COLLECTION
18
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer New 102
Epoch Table
X
CMU 15-721 (Spring 2016)
BW-TREE: STRUCTURE MODIFICATIONS
Page sizes are elastic → No hard physical threshold for splitting. → This allows the tree to split a page when convenient.
Tree supports “half-split” without latching → Install split at child level by creating new page → Install new separator key and pointer at parent level
19
CMU 15-721 (Spring 2016)
102 104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
105
CMU 15-721 (Spring 2016)
102 104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
CMU 15-721 (Spring 2016)
102 104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Split
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Split
X X
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Split
X X
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Split
X X
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Split
X X
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Split
X X
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Split
X X
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Separator
▲Split
X X
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Separator
▲Split
X X
[∞,3) [3,7) [7,∞)
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Separator
▲Split
X X
[∞,3) [3,7) [7,∞)
[5,7)
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Separator
▲Split
X X
[∞,3) [3,7) [7,∞)
[5,7)
CMU 15-721 (Spring 2016)
102
105
104
101
103
BW-TREE: STRUCTURE MODIFICATIONS
20
Mapping Table
PID Addr
101
102
103
104
Logical Pointer Physical Pointer
3 4 5 6 1 2 7 8 105
5 6
▲Separator
▲Split
X X
[∞,3) [3,7) [7,∞)
[5,7)
CMU 15-721 (Spring 2016)
BW-TREE: PERFORMANCE
21
Source: Justin Levandoski
10.4
3.83 2.84
0.56 0.66 0.33
4.23
1.02 0.72
0
2
4
6
8
10
12
Xbox Synthetic Deduplication
Oper
atio
ns/s
ec (M
)
Bw-Tree B+Tree Skip List
CMU 15-721 (Spring 2016)
CONCURRENT SKIP L IST
Can implement insert and delete without locks using only CAS operations. Perform lazy deletion of towers.
22
CONCURRENT MAINTENANCE OF SKIP LISTS Univ. of Maryland Tech Report 1990
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End Levels
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
SKIP L ISTS: INSERT
23
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Insert K5
K5
K5
K5 V5
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: DELETE
24
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Delete K5
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: DELETE
24
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Delete K5
Del false
Del false
Del false
Del false
Del false
Del false
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: DELETE
24
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Delete K5
Del false
Del false
Del false
Del false
Del false
Del false
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: DELETE
24
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Delete K5
Del false
Del false
Del false
Del false
Del false
Del false
Del true
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: DELETE
24
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Delete K5
Del false
Del false
Del false
Del false
Del false
Del false
Del true
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: DELETE
24
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Delete K5
Del false
Del false
Del false
Del false
Del false
Del false
Del true
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: DELETE
24
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Delete K5
Del false
Del false
Del false
Del false
Del false
Del false
Del true
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: DELETE
24
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Delete K5
Del false
Del false
Del false
Del false
Del false
Del false
Del true
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K6 V6
Levels
SKIP L ISTS: DELETE
24
∞
∞
∞
P=N
P=N/2
P=N/4
Operation: Delete K5
Del false
Del false
Del false
Del false
Del false
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Stack:
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Stack:
K2
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Stack:
K2
K3
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Stack:
K2
K4 K3
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Stack:
K2
K4 K3
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Stack:
K2
K4 K3
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Stack:
K2
K4 K3
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
End
K1 V1
K2
K2 V2
K3 V3
K4 V4
K4
K5 V5
K5
K5
K6 V6
Levels
SKIP L ISTS: REVERSE SEARCH
25
∞
∞
∞
P=N
P=N/2
P=N/4
Txn #1: Find [K4,K2]
K2<K5
K2=K2
Stack:
K2
K4 K3
K2<K4
Source: Mark Papadakis
CMU 15-721 (Spring 2016)
ADAPATIVE RADIX TREE (ART)
Uses a digital representation of keys to examine key prefixes one-by-one instead of comparing the entire key. Radix trees properties: → The height of the tree depends on the length of keys. → Does not require rebalancing → The path to a leaf node represents the key of the leaf → Keys are stored implicitly and can be reconstructed
from paths.
26
THE ADAPTIVE RADIX TREE: ARTFUL INDEXING FOR MAIN-MEMORY DATABASES ICDE 2013
CMU 15-721 (Spring 2016)
TRIE VS. RADIX TREE
27
Keys: hello, hat, have
Trie
E H
L
¤
L O
A
¤ T
¤
V
E
Radix Tree
ELLO H
¤
A
¤ T
¤
VE
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
¤ ¤
T VE
H
A
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
¤ ¤
T VE
H
A
Operation: Insert hair
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
¤ ¤
T VE
H
A
¤
IR
Operation: Insert hair
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
¤ ¤
T VE
H
A
¤
IR
Operation: Insert hair Operation: Delete hat, have
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
¤ ¤
T VE
H
A
¤
IR
Operation: Insert hair Operation: Delete hat, have
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
¤ ¤
T VE
H
A
¤
IR
Operation: Insert hair Operation: Delete hat, have
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
H
A
¤
IR
Operation: Insert hair Operation: Delete hat, have
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
H
A
¤
IR
Operation: Insert hair Operation: Delete hat, have
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
H
A
Operation: Insert hair Operation: Delete hat, have
AIR
¤
CMU 15-721 (Spring 2016)
ART INDEX: MODIFICATIONS
28
¤
ELLO
H
A
Operation: Insert hair Operation: Delete hat, have
AIR
¤ Note: The ART index described in 2013 is not latch-free.
CMU 15-721 (Spring 2016)
ART INDEX: B INARY COMPARABLE KEYS
Not all attribute types can be decomposed into binary comparable digits for a radix tree. → Unsigned Integers: Byte order must be flipped for
little endian machines. → Signed Integers: Flip two’s-complement so that
negative numbers are smaller than positive. → Floats: Classify into group (neg vs. pos, normalized
vs. denormalized), then store as unsigned integer. → Compound: Transform each attribute separately.
29
CMU 15-721 (Spring 2016)
PARTING THOUGHTS
Bw-Tree is probably the most dank database data structure in recent years. Skip List is really easy to implement.
30
CMU 15-721 (Spring 2016)
NEXT CLASS
Indexing for OLAP workloads. → More from Microsoft Research…
Project #2 Announcement
31
Recommended