54 SKIP LISTS: DELETE Delete K5 Levels End ∞ K5 P=N/4 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N Del Del Del Del Del Del Del V1 V2 V3 V4 V5 V6 false false false false false true false
55 SKIP LISTS: DELETE Delete K5 Levels End ∞ K5 P=N/4 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N Del Del Del Del Del Del Del V1 V2 V3 V4 V5 V6 false false false false false true false
56 SKIP LISTS: DELETE Delete K5 Levels End ∞ K5 P=N/4 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N Del Del Del Del Del Del Del V1 V2 V3 V4 V5 V6 false false false false false true false
57 SKIP LISTS: DELETE Delete K5 Levels End ∞ K5 P=N/4 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N Del Del Del Del Del Del Del V1 V2 V3 V4 V5 V6 false false false false false true false
58 SKIP LISTS: DELETE Delete K5 Levels End ∞ P=N/4 ∞ K2 K4 P=N/2 ∞ K1 K2 K3 K4 K6 P=N Del Del Del Del Del V1 V2 V3 V4 V6 false false false false false
59 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.
60 SKIP LIST OPTIMIZATIONS Reducing RAND() invocations. Packing multiple keys in a node. Reverse iteration with a stack. Reusing nodes with memory pools. SKIP LISTS: DONE RIGHT Ticki(?) Blog 2016
61 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. K2 K3 K6 V2 V3 V6 Source: Ticki
62 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. K2 K3 K6 - V2 V3 V6 - Source: Ticki
63 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. Insert K4 K2 K3 K6 - V2 V3 V6 - Source: Ticki
64 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. Insert K4 K2 K3 K6 - V2 V3 V6 - Source: Ticki
65 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. Insert K4 K2 K3 K6 K4 - V2 V3 V6 V4 - Source: Ticki
66 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. Search K6 K2 K3 K6 K4 - V2 V3 V6 V4 - Source: Ticki
67 SKIP LISTS: REVERSE SEARCH Find [K4,K2] Levels End ∞ K5 P=N/4 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
68 SKIP LISTS: REVERSE SEARCH Find [K4,K2] Levels End ∞ K5 P=N/4 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
69 SKIP LISTS: REVERSE SEARCH Find [K4,K2] Levels End K2<K5 ∞ K5 P=N/4 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
70 SKIP LISTS: REVERSE SEARCH Find [K4,K2] Levels End K2<K5 ∞ K5 P=N/4 K2=K2 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
71 SKIP LISTS: REVERSE SEARCH Find [K4,K2] Levels End K2<K5 ∞ K5 P=N/4 K2=K2 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
72 SKIP LISTS: REVERSE SEARCH Stack: Find [K4,K2] Levels End K2<K5 ∞ K5 P=N/4 K2=K2 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
73 SKIP LISTS: REVERSE SEARCH Stack: Find [K4,K2] Levels End K2<K5 K2 ∞ K5 P=N/4 K2=K2 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
74 SKIP LISTS: REVERSE SEARCH Stack: Find [K4,K2] Levels End K3 K2<K5 K2 ∞ K5 P=N/4 K2=K2 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
75 SKIP LISTS: REVERSE SEARCH Stack: Find [K4,K2] K4 Levels End K3 K2<K5 K2 ∞ K5 P=N/4 K2=K2 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
76 SKIP LISTS: REVERSE SEARCH Stack: Find [K4,K2] K4 Levels End K3 K2<K5 K2 ∞ K5 P=N/4 K2=K2 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
77 SKIP LISTS: REVERSE SEARCH Stack: Find [K4,K2] K4 Levels End K3 K2<K5 K2 ∞ K5 P=N/4 K2=K2 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
78 SKIP LISTS: REVERSE SEARCH Stack: Find [K4,K2] K4 Levels End K3 K2<K5 K2 ∞ K5 P=N/4 K2=K2 ∞ K2 K4 K5 P=N/2 ∞ K1 K2 K3 K4 K5 K6 P=N V1 V2 V3 V4 V5 V6 Source: Mark Papadakis
79 OBSERVATION Because CaS only updates a single address at a time, this limits the design of our data structures → We cannot have reverse pointers in a latch-free concurrent Skip List. → We cannot build a latch-free B+Tree. What if we had an indirection layer that allowed us to update multiple addresses atomically?
80 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. THE BW-TREE: A B-TREE FOR NEW HARDWARE ICDE 2013
81 BW-TREE: MAPPING TABLE Mapping Table Index Page PID Addr 101 102 103 104 Logical Pointer Physical Pointer
82 BW-TREE: MAPPING TABLE Mapping Table Index Page PID Addr 101 101 102 103 102 104 104 Logical Pointer Physical Pointer
83 BW-TREE: MAPPING TABLE Mapping Table Index Page PID Addr 101 101 102 103 102 104 104 Logical Pointer Physical Pointer
84 BW-TREE: MAPPING TABLE Mapping Table Index Page PID Addr 101 102 103 104 Logical Pointer Physical Pointer
85 BW-TREE: MAPPING TABLE Mapping Table Index Page PID Addr 102 104 101 102 103 102 104 104 Logical Pointer Physical Pointer
86 BW-TREE: DELTA UPDATES Mapping Table PID Addr 101 102 103 104 Page 102 Logical Pointer Physical Pointer Source: Justin Levandoski
87 BW-TREE: DELTA UPDATES Mapping Table Each update to a page produces a new delta. PID Addr 101 102 103 104 Page 102 Logical Pointer Physical Pointer Source: Justin Levandoski
88 BW-TREE: DELTA UPDATES Mapping Table Each update to a page produces a new delta. PID Addr 101 102 ▲ Insert 50 103 104 Page 102 Logical Pointer Physical Pointer Source: Justin Levandoski
89 BW-TREE: DELTA UPDATES Mapping Table Each update to a page produces a new delta. PID Addr 101 Delta physically points to 102 base page. ▲ Insert 50 103 104 Page 102 Logical Pointer Physical Pointer Source: Justin Levandoski
90 BW-TREE: DELTA UPDATES Mapping Table Each update to a page produces a new delta. PID Addr 101 Delta physically points to 102 base page. ▲ Insert 50 103 Install delta address in 104 physical address slot of Page 102 Logical mapping table using CAS. Pointer Physical Pointer Source: Justin Levandoski
91 BW-TREE: DELTA UPDATES Mapping Table Each update to a page produces a new delta. PID Addr 101 Delta physically points to 102 base page. ▲ Insert 50 103 Install delta address in 104 physical address slot of Page 102 Logical mapping table using CAS. Pointer Physical Pointer Source: Justin Levandoski
92 BW-TREE: DELTA UPDATES Mapping Table Each update to a page produces a new delta. PID Addr 101 Delta physically points to 102 base page. ▲ Insert 50 103 Install delta address in 104 physical address slot of Page 102 Logical mapping table using CAS. Pointer Physical Pointer Source: Justin Levandoski
93 BW-TREE: DELTA UPDATES Mapping Table Each update to a page produces a new delta. ▲ Delete 48 PID Addr 101 Delta physically points to 102 base page. ▲ Insert 50 103 Install delta address in 104 physical address slot of Page 102 Logical mapping table using CAS. Pointer Physical Pointer Source: Justin Levandoski
94 BW-TREE: DELTA UPDATES Mapping Table Each update to a page produces a new delta. ▲ Delete 48 PID Addr 101 Delta physically points to 102 base page. ▲ Insert 50 103 Install delta address in 104 physical address slot of Page 102 Logical mapping table using CAS. Pointer Physical Pointer Source: Justin Levandoski
95 BW-TREE: SEARCH Mapping Table ▲ Delete 48 PID Addr 101 102 ▲ Insert 50 103 104 Page 102 Logical Pointer Physical Pointer
96 BW-TREE: SEARCH Mapping Table Traverse tree like a regular B+tree. ▲ Delete 48 PID Addr 101 102 ▲ Insert 50 103 104 Page 102 Logical Pointer Physical Pointer
97 BW-TREE: SEARCH Mapping Table Traverse tree like a regular B+tree. ▲ Delete 48 PID Addr 101 If mapping table points to 102 delta chain, stop at first ▲ Insert 50 103 occurrence of search key. 104 Page 102 Logical Pointer Physical Pointer
98 BW-TREE: SEARCH Mapping Table Traverse tree like a regular B+tree. ▲ Delete 48 PID Addr 101 If mapping table points to 102 delta chain, stop at first ▲ Insert 50 103 occurrence of search key. 104 Otherwise, perform binary Page 102 Logical search on base page. Pointer Physical Pointer
99 BW-TREE: CONTENTION UPDATES Mapping Table PID Addr 101 102 ▲ Insert 50 103 104 Page 102 Logical Pointer Physical Pointer
100 BW-TREE: CONTENTION UPDATES Mapping Table PID Addr 101 Threads may try to install 102 updates to same state of the ▲ Insert 50 103 page. 104 Page 102 Logical Pointer Physical Pointer
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