Lock-free Concurrent Level Hashing for Persistent Memory Zhangyu - PowerPoint PPT Presentation

Level Hashing [OSDI ’18]  PM-friendly hashing index − Two-level bucketized hash table with one- step movement A 4-slot bucket key Tokens h 1 (key) h 2 (key) KV1 KV2 ... Top level Slots KV3 0 1 2N-2 2N-1 KV4 Two-level structure One-step movement ... Bottom level One extra write at most 0 N-1 10

Level Hashing [OSDI ’18]  PM-friendly hashing index − Two-level bucketized hash table with one-  Write efficiency step movement A 4-slot bucket key Tokens h 1 (key) h 2 (key) KV1 KV2 ... Top level Slots KV3 0 1 2N-2 2N-1 KV4 Two-level structure One-step movement ... Bottom level One extra write at most 0 N-1 10

Level Hashing [OSDI ’18]  PM-friendly hashing index − Two-level bucketized hash table with one-  Write efficiency step movement − Low-overhead consistency guarantee via  Crash consistency atomic token update A 4-slot bucket key Tokens (Atomic update) h 1 (key) h 2 (key) KV1 KV2 ... Top level Slots KV3 0 1 2N-2 2N-1 KV4 Two-level structure One-step movement ... Bottom level One extra write at most 0 N-1 10

Level Hashing [OSDI ’18]  PM-friendly hashing index − Two-level bucketized hash table with one-  Write efficiency step movement − Low-overhead consistency guarantee via  Crash consistency atomic token update − Rehashing 1/3 buckets for one resizing ... Top level 0 1 2N-2 2N-1 ... Bottom level 0 N-1 10

Level Hashing [OSDI ’18]  PM-friendly hashing index − Two-level bucketized hash table with one-  Write efficiency step movement − Low-overhead consistency guarantee via  Crash consistency atomic token update − Rehashing 1/3 buckets for one resizing ... Top level 0 1 2 4N-3 4N-2 4N-1 ... Bottom level 0 1 2N-2 2N-1 10

Concurrency in Level Hashing  Slot-grained lock for queries  Single-thread blocking resizing Thread-1: search(x) Thread-2: insert(key) x ... Top level 0 1 2N-2 2N-1 ... Top level 0 1 2N-2 2N-1 ... Bottom level ... Bottom level 0 N-1 0 N-1 11

Concurrency in Level Hashing  Slot-grained lock for queries  Single-thread blocking resizing Thread-1: search(x) Thread-2: insert(key) Thread-1: search x x ... Top level 0 1 2N-2 2N-1 ... Top level Thread-2: relocate x 0 1 2N-2 2N-1 ... Bottom level ... Bottom level 0 N-1 0 N-1 11

Concurrency in Level Hashing  Slot-grained lock for queries  Single-thread blocking resizing Thread-1: search(x) Thread-2: insert(key) Thread-1: search x No “x” is found x ... Top level 0 1 2N-2 2N-1 ... Top level Thread-2: relocate x 0 1 2N-2 2N-1 ... Bottom level ... Bottom level 0 N-1 0 N-1 Missing inserted items! 11

Concurrency in Level Hashing  Slot-grained lock for queries  Single-thread blocking resizing Thread-1: search(x) Thread-2: insert(key) Thread-1: search x Thread-1: insert(key) and trigger resizing… No “x” is found x ... ... Top level 0 1 2 4N-3 4N-2 4N-1 0 1 2N-2 2N-1 ... Top level Thread-2: relocate x 0 1 2N-2 2N-1 ... Bottom level ... Bottom level 0 N-1 0 N-1 Missing inserted items! 11

Concurrency in Level Hashing  Slot-grained lock for queries  Single-thread blocking resizing Thread-1: search(x) Thread-2~n: wait for finishing resizing… Thread-2: insert(key) Thread-1: search x Thread-1: insert(key) and trigger resizing… No “x” is found x ... ... Top level 0 1 2 4N-3 4N-2 4N-1 0 1 2N-2 2N-1 ... Top level Thread-2: relocate x 0 1 2N-2 2N-1 ... Bottom level ... Bottom level 0 N-1 0 N-1 Missing inserted items! Resizing blocks queries! 11

Concurrency in Level Hashing  Slot-grained lock for queries  Single-thread blocking resizing Thread-1: search(x) Thread-2~n: wait for finishing resizing… Thread-2: insert(key) Thread-1: search x Thread-1: insert(key) and trigger resizing… No “x” is found x ... ... Top level 0 1 2 4N-3 4N-2 4N-1 0 1 2N-2 2N-1 ... Top level Concurrency is the bottleneck Thread-2: relocate x 0 1 2N-2 2N-1 ... Bottom level ... Bottom level 0 N-1 0 N-1 Missing inserted items! Resizing blocks queries! 11

Challenges for PM Hashing  Challenges − Performance degradation for blocking resizing • High latency for coarse-grained locks − Limited scalability for lock-based concurrency control • Lock constraint for concurrent accesses • Persisting overheads in the critical path  Design goals − A PM-friendly and high-concurrency hashing scheme 12

Our Approach: Clevel Hashing key H 1 (key) H 2 (key) ... 0 1 2 2N-3 2N-2 2N-1 ... Level list 0 1 N-2 N-1 Rehashing ... ... ... last_level Context first_level is_resizing Global context ptr. Rehashing threads Worker threads A thread ... ... Thread-local context ptr. 13

Our Approach: Clevel Hashing  Dynamic multi-level structure w/o key H 1 (key) H 2 (key) ... extra writes for insertion 0 1 2 2N-3 2N-2 2N-1  Write-optimal insertion ... Level list 0 1 N-2 N-1 Rehashing ... ... ... last_level Context first_level is_resizing Global context ptr. Rehashing threads Worker threads A thread ... ... Thread-local context ptr. 13

Our Approach: Clevel Hashing  Dynamic multi-level structure w/o key H 1 (key) H 2 (key) ... extra writes for insertion 0 1 2 2N-3 2N-2 2N-1  Write-optimal insertion ... Level list 0 1 N-2 N-1 Rehashing ... ...  Asynchronous rehashing w/o ... blocking concurrent queries  Non-blocking resizing last_level Context first_level is_resizing Global context ptr. Rehashing threads Worker threads A thread ... ... Thread-local context ptr. 13

Our Approach: Clevel Hashing  Dynamic multi-level structure w/o key H 1 (key) H 2 (key) ... extra writes for insertion 0 1 2 2N-3 2N-2 2N-1  Write-optimal insertion ... Level list 0 1 N-2 N-1 Rehashing ... ...  Asynchronous rehashing w/o ... blocking concurrent queries  Non-blocking resizing last_level Context first_level is_resizing Global context ptr.  Lock-free concurrency control Rehashing threads Worker threads A thread ... ...  Lock-free queries Thread-local context ptr. 13

Components  Dynamic Multi-level Structure  Non-blocking Resizing  Lock-free Concurrency Control 14

Components  Dynamic Multi-level Structure  Non-blocking Resizing  Lock-free Concurrency Control 15

Dynamic Multi-level Structure  Support for variable-length items − Store pointers in slots and actual items outside of the table 16

Dynamic Multi-level Structure  Support for variable-length items  Write-optimized hash table − 8 slots per bucket ... A bucket ... KV_PTR1 KV_PTR8 Slots (each 8 bytes) 17

Dynamic Multi-level Structure  Support for variable-length items key  Write-optimized hash table H 1 (key) H 2 (key) − 8 slots per bucket ... − 2 candidate buckets in one level 18

Dynamic Multi-level Structure  Support for variable-length items key  Write-optimized hash table H 1 (key) H 2 (key) − 8 slots per bucket ... − 2 candidate buckets in one level 0 1 2 2N-3 2N-2 2N-1 ... − Sharing-based multiple levels 0 1 N-2 N-1 • Add a level for resizing ... • Remove one when rehashing completes ... 19

Dynamic Multi-level Structure  Support for variable-length items key  Write-optimized hash table H 1 (key) H 2 (key) − 8 slots per bucket ... − 2 candidate buckets in one level 0 1 2 2N-3 2N-2 2N-1 ... − Sharing-based multiple levels 0 1 N-2 N-1 • Add a level for resizing ... • Remove one when rehashing completes ... No extra writes for insertion Write-optimal 19

Components  Dynamic Multi-level Structure  Non-blocking Resizing  Lock-free Concurrency Control 20

The Support for Concurrent Resizing key H 1 (key) H 2 (key) ... 0 1 2 2N-3 2N-2 2N-1 ... 0 1 N-2 N-1 ... ... 21

The Support for Concurrent Resizing  Level list key H 1 (key) H 2 (key) − A linked list to associate levels ... 0 1 2 2N-3 2N-2 2N-1 ... Level list 0 1 N-2 N-1 ... ... ... 21

The Support for Concurrent Resizing  Level list key H 1 (key) H 2 (key) − A linked list to associate levels ... 0 1 2 2N-3 2N-2 2N-1 ... Level list 0 1 N-2 N-1  Context ... ... − A metadata structure including: ... • first_level (the largest level) last_level first_level Context • last_level is_resizing Global context ptr. • is_resizing 22

Non-blocking Resizing  Resizing steps 1. Make a local copy of the global context pointer key H 1 (key) H 2 (key) ... Level list 0 1 N-2 N-1 ... ... ... last_level first_level Context is_resizing Global context ptr. Worker threads A thread ... Thread-local context ptr. 1 23

Non-blocking Resizing  Resizing steps key H 1 (key) H 2 (key) 1. Make a local copy of the global context pointer 2 ... 2. CAS to append a new level 0 1 2 2N-3 2N-2 2N-1 ... Level list 0 1 N-2 N-1 ... ... ... last_level Context first_level is_resizing Global context ptr. Worker threads A thread ... Thread-local context ptr. 1 24

Non-blocking Resizing  Resizing steps key H 1 (key) H 2 (key) 1. Make a local copy of the global context pointer 2 ... 2. CAS to append a new level 0 1 2 2N-3 2N-2 2N-1 ... Level list 3. CoW + CAS to update the first_level 0 1 N-2 N-1 ... ... ... last_level 8 B last_level first_level Context 8 B 3 first_level is_resizing Lightweight CoW 1 B is_resizing Global context ptr. Context size: 17 bytes Worker threads A thread ... Thread-local context ptr. 1 25

Non-blocking Resizing  Resizing steps key H 1 (key) H 2 (key) 1. Make a local copy of the global context pointer 2 ... 2. CAS to append a new level 0 1 2 2N-3 2N-2 2N-1 ... Level list 3. CoW + CAS to update the first_level 0 1 N-2 N-1 Rehashing 4. Rehash items in the last level ... ... 4 ... last_level Context first_level 3 is_resizing Global context ptr. Worker threads A thread ... Thread-local context ptr. 1 26

Non-blocking Resizing  Resizing steps key H 1 (key) H 2 (key) 1. Make a local copy of the global context pointer 2 ... 2. CAS to append a new level 0 1 2 2N-3 2N-2 2N-1 ... Level list 3. CoW + CAS to update the first_level 0 1 N-2 N-1 Rehashing 4. Rehash items in the last level ... ... 4 5. CoW + CAS to update the last_level ... 5 last_level first_level Context 3 is_resizing Global context ptr. Worker threads A thread ... Thread-local context ptr. 1 27

Non-blocking Resizing  Resizing steps key H 1 (key) H 2 (key) 1. Make a local copy of the global context pointer ... 2. CAS to append a new level 0 1 2 2N-3 2N-2 2N-1 ... Level list 3. CoW + CAS to update the first_level 0 1 N-2 N-1 Rehashing 4. Rehash items in the last level ... ... 5. CoW + CAS to update the last_level ... last_level first_level Context is_resizing Global context ptr. 28

Non-blocking Resizing  Resizing steps key H 1 (key) H 2 (key) 1. Make a local copy of the global context pointer ... Expansion 2. CAS to append a new level 0 1 2 2N-3 2N-2 2N-1 stage ... Level list 3. CoW + CAS to update the first_level 0 1 N-2 N-1 Rehashing Rehashing 4. Rehash items in the last level ... ... stage 5. CoW + CAS to update the last_level ... last_level first_level Context is_resizing Global context ptr. Queries Expansion stage Rehashing stage Resizing steps 28

Non-blocking Resizing  Resizing steps key H 1 (key) H 2 (key) 1. Make a local copy of the global context pointer ... Expansion 2. CAS to append a new level 0 1 2 2N-3 2N-2 2N-1 stage ... Level list 3. CoW + CAS to update the first_level 0 1 N-2 N-1 Rehashing Rehashing 4. Rehash items in the last level ... ... stage 5. CoW + CAS to update the last_level ...  Non-blocking resizing scheme − Rehashing threads: rehash until there are 2 last_level first_level Context levels left is_resizing Global context ptr. Queries Rehashing threads (background) Expansion stage Rehashing stage Resizing steps 28

Non-blocking Resizing  Resizing steps key H 1 (key) H 2 (key) 1. Make a local copy of the global context pointer ... Expansion 2. CAS to append a new level 0 1 2 2N-3 2N-2 2N-1 stage ... Level list 3. CoW + CAS to update the first_level 0 1 N-2 N-1 Rehashing Rehashing 4. Rehash items in the last level ... ... stage 5. CoW + CAS to update the last_level ...  Non-blocking resizing scheme − Rehashing threads: rehash until there are 2 last_level first_level Context levels left is_resizing Global context ptr. Queries Worker threads Rehashing threads (background) Expansion stage Rehashing stage Resizing steps 28

Components  Dynamic Multi-level Structure  Non-blocking Resizing  Lock-free Concurrency Control 29

Lock-free Search  High latency for pointer dereference 30

Lock-free Search  High latency for pointer dereference − Summary tags ... A bucket KV_PTR1 KV_PTR8 • A tag is the summary for a key A slot • Leverage the unused 16 highest bits of Tag (2 B) a pointer in x86_64 to store the tag Update tag and pointer in an atomic manner 30

Lock-free Search  High latency for pointer dereference : a pointer in one slot − Summary tags key H 1 (key) H 2 (key) • A tag is the summary for a key ... • Leverage the unused 16 highest bits of 0 1 2 2N-3 2N-2 2N-1 ... Level list a pointer in x86_64 to store the tag 0 1 N-2 N-1 ... ... ... ...  Missing items due to rehashing 31

Lock-free Search  High latency for pointer dereference : a pointer in one slot − Summary tags Thread-1: search key H 1 (key) H 2 (key) • A tag is the summary for a key ... ... • Leverage the unused 16 highest bits of 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 ... Level list a pointer in x86_64 to store the tag 0 1 N-2 N-1 Missing ... ... ...  Missing items due to rehashing Thread-2: rehashing 31

Lock-free Search  High latency for pointer dereference : a pointer in one slot − Summary tags key H 1 (key) H 2 (key) • A tag is the summary for a key ... ... • Leverage the unused 16 highest bits of 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 ... Level list a pointer in x86_64 to store the tag 0 1 N-2 N-1 ... ... ...  Missing items due to rehashing Thread-2: rehashing Thread-1: b2t search − Bottom-to-top (b2t) search • Search from the last level to the first level • Redo the search when no item is found and the context changes 31

Lock-free Insertion  Basic workflow − Allocate the new item in PM − B2t search to find duplicate keys − Insert the pointer via CAS ... 0 1 2 2N-3 2N-2 2N-1 ... Level list 0 1 N-2 N-1 ... ... ... 32

Lock-free Insertion  Basic workflow − Allocate the new item in PM − B2t search to find duplicate keys − Insert the pointer via CAS  Duplicate items from concurrent insertions x H 1 (x) H 2 (x) ... 0 1 2 2N-3 2N-2 2N-1 ... Level list 0 1 N-2 N-1 ... ... ... 32

Lock-free Insertion  Basic workflow − Allocate the new item in PM − B2t search to find duplicate keys − Insert the pointer via CAS  Duplicate items from concurrent insertions Thread-1: Thread-2: insert(x) insert(x) − Both items are allowed for read ... ... − Fix duplication in future update and deletion 0 1 2 2N-3 2N-2 2N-1 ... Level list 0 1 N-2 N-1 ... ... ... 32

Lock-free Insertion  Basic workflow − Allocate the new item in PM − B2t search to find duplicate keys − Insert the pointer via CAS  Duplicate items from concurrent insertions − Both items are allowed for read ... − Fix duplication in future update and deletion 0 1 2 2N-3 2N-2 2N-1 ... Level list  Loss of new items due to rehashing 0 1 N-2 N-1 ... ... ... Thread-1: Thread-2: insert(x) rehashing 32

Lock-free Insertion  Basic workflow − Allocate the new item in PM − B2t search to find duplicate keys − Insert the pointer via CAS  Duplicate items from concurrent insertions − Both items are allowed for read ... − Fix duplication in future update and deletion 0 1 2 2N-3 2N-2 2N-1 ... Level list  Loss of new items due to rehashing 0 1 N-2 N-1 ... ... ... ... Thread-1: Thread-2: insert(x) rehashing 32

Lock-free Insertion  Basic workflow − Allocate the new item in PM − B2t search to find duplicate keys − Insert the pointer via CAS  Duplicate items from concurrent insertions − Both items are allowed for read ... − Fix duplication in future update and deletion 0 1 2 2N-3 2N-2 2N-1 ... Level list  Loss of new items due to rehashing 0 1 N-2 N-1 ... ... ... ... Thread-1: Thread-2: insert(x) rehashing 32

Lock-free Insertion  Basic workflow − Allocate the new item in PM − B2t search to find duplicate keys − Insert the pointer via CAS  Duplicate items from concurrent insertions − Both items are allowed for read ... − Fix duplication in future update and deletion 0 1 2 2N-3 2N-2 2N-1 ... Level list  Loss of new items due to rehashing 0 1 N-2 N-1 ... ... Thread-1: insert(x) 32

Lock-free Insertion  Basic workflow − Allocate the new item in PM − B2t search to find duplicate keys − Insert the pointer via CAS  Duplicate items from concurrent insertions − Both items are allowed for read ... − Fix duplication in future update and deletion 0 1 2 2N-3 2N-2 2N-1 ... Level list  Loss of new items due to rehashing 0 1 N-2 N-1 ... ... Loss Thread-1: insert(x) 32

Lock-free Insertion  Basic workflow − Allocate the new item in PM − B2t search to find duplicate keys − Insert the pointer via CAS  Duplicate items from concurrent insertions − Both items are allowed for read ... − Fix duplication in future update and deletion 0 1 2 2N-3 2N-2 2N-1 ... Level list  Loss of new items due to rehashing 0 1 N-2 N-1 ... ... − Context-aware insertion Loss • Not inserted to the rehashed last level Thread-1: insert(x) • Redo insertion for possible loss 32

Lock-free Update  Inconsistency for duplicate items 33

Lock-free Update  Inconsistency for duplicate items − Concurrent insertions with the same key Thread-1: Thread-2: insert(x) insert(x) ... ... 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 ... Level list 0 1 N-2 N-1 ... ... ... 33

Lock-free Update  Inconsistency for duplicate items − Concurrent insertions with the same key − Retry of context-aware insertion Thread-1: Thread-2: Thread-1: insert(x) insert(x) redo insert(x) ... ... ... ... 0 1 2 2N-3 2N-2 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 1 2 2N-3 2N-2 2N-1 ... ... Level list Level list 0 1 N-2 N-1 0 1 N-2 N-1 ... ... ... ... ... ... ... Thread-1: insert(x) 33

Lock-free Update  Inconsistency for duplicate items − Concurrent insertions with the same key − Retry of context-aware insertion − Data movement for rehashing Thread-1: Thread-2: Thread-1: insert(x) insert(x) redo insert(x) ... ... ... ... ... ... 0 1 2 2N-3 2N-2 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 1 2 2N-3 2N-2 2N-1 ... ... ... Level list Level list Level list 0 1 N-2 N-1 0 1 N-2 N-1 0 1 N-2 N-1 Rehashing ... ... ... ... thread ... ... ... ... ... ... ... Thread-1: insert(x) 33

Lock-free Update  Inconsistency for duplicate items − Concurrent insertions with the same key − Retry of context-aware insertion − Data movement for rehashing Thread-1: Thread-2: Thread-1: insert(x) insert(x) redo insert(x) ... ... ... ... ... ... 0 1 2 2N-3 2N-2 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 1 2 2N-3 2N-2 2N-1 ... ... ... Level list Level list Level list 0 1 N-2 N-1 0 1 N-2 N-1 0 1 N-2 N-1 Rehashing ... ... ... ... thread ... ... ... ... ... ... ... Thread-1: insert(x) Two pointers to different items 33

Lock-free Update  Inconsistency for duplicate items − Concurrent insertions with the same key − Retry of context-aware insertion − Data movement for rehashing Thread-1: Thread-2: Thread-1: insert(x) insert(x) redo insert(x) ... ... ... ... ... ... 0 1 2 2N-3 2N-2 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 1 2 2N-3 2N-2 2N-1 ... ... ... Level list Level list Level list 0 1 N-2 N-1 0 1 N-2 N-1 0 1 N-2 N-1 Rehashing ... ... ... ... thread ... ... ... ... ... ... ... Thread-1: insert(x) Two pointers to different items Two pointers to the same item 33

Lock-free Update  Content-conscious Find  Inconsistency for duplicate items − B2t search to find two pointers to duplicate − Concurrent insertions with the same key items − Retry of context-aware insertion − Data movement for rehashing Thread-1: Thread-2: Thread-1: insert(x) insert(x) redo insert(x) ... ... ... ... ... ... 0 1 2 2N-3 2N-2 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 1 2 2N-3 2N-2 2N-1 ... ... ... Level list Level list Level list 0 1 N-2 N-1 0 1 N-2 N-1 0 1 N-2 N-1 Rehashing ... ... ... ... thread ... ... ... ... ... ... ... Thread-1: B2t insert(x) search Two pointers to different items Two pointers to the same item 33

Lock-free Update  Content-conscious Find  Inconsistency for duplicate items − B2t search to find two pointers to duplicate − Concurrent insertions with the same key items − Retry of context-aware insertion − Check if two pointers refer to the same item − Data movement for rehashing Thread-1: Thread-2: Thread-1: insert(x) insert(x) redo insert(x) ... ... ... ... ... ... 0 1 2 2N-3 2N-2 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 1 2 2N-3 2N-2 2N-1 ... ... ... Level list Level list Level list 0 1 N-2 N-1 0 1 N-2 N-1 0 1 N-2 N-1 Rehashing ... ... ... ... thread ... ... ... ... ... ... ... Thread-1: B2t insert(x) search Two pointers to different items Two pointers to the same item 33

Lock-free Update  Content-conscious Find  Inconsistency for duplicate items − B2t search to find two pointers to duplicate − Concurrent insertions with the same key items − Retry of context-aware insertion − Check if two pointers refer to the same item − Data movement for rehashing • Yes : delete the first pointer matching the key Thread-1: Thread-2: Thread-1: insert(x) insert(x) redo insert(x) ... ... ... ... ... ... 0 1 2 2N-3 2N-2 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 1 2 2N-3 2N-2 2N-1 ... ... ... Level list Level list Level list 0 1 N-2 N-1 0 1 N-2 N-1 0 1 N-2 N-1 Rehashing ... ... ... ... thread ... ... ... ... ... B2t search Two pointers to different items Two pointers to the same item 33

Lock-free Update  Content-conscious Find  Inconsistency for duplicate items − B2t search to find two pointers to duplicate − Concurrent insertions with the same key items − Retry of context-aware insertion − Check if two pointers refer to the same item − Data movement for rehashing • Yes : delete the first pointer matching the key • No : delete the first pointer and corresponding item matching the key Thread-2: Thread-1: insert(x) redo insert(x) ... ... ... ... ... ... ... 0 1 2 2N-3 2N-2 2N-1 0 0 1 1 2 2 2N-3 2N-3 2N-2 2N-2 2N-1 2N-1 0 0 0 1 1 1 2 2 2 2N-3 2N-3 2N-3 2N-2 2N-2 2N-2 2N-1 2N-1 2N-1 0 1 2 2N-3 2N-2 2N-1 ... ... ... Level list Level list Level list 0 1 N-2 N-1 0 1 N-2 N-1 0 1 N-2 N-1 Rehashing ... ... ... ... thread ... ... ... ... ... B2t search Two pointers to different items Two pointers to the same item 33

Failures of Lock-free Update  Update failures due to interleaved update and rehashing ... 0 1 2 2N-3 2N-2 2N-1 ... Level list 0 1 N-2 N-1 ... ... ... ... Thread 1: update Thread-2: rehashing Timeline 34

Failures of Lock-free Update  Update failures due to interleaved update and rehashing ... 0 1 2 2N-3 2N-2 2N-1 ... Level list 0 1 N-2 N-1 ... ... ... ... Find Thread 1: update Thread-2: rehashing Timeline 34