A Parallel Compact Hash Table Alfons Laarman & Steven van der - PowerPoint PPT Presentation

A Parallel Compact Hash Table Alfons Laarman & Steven van der Vegt

Overview Research Motivation Background Contribution A Parallel Compact Hash Table October 3, 2011 2 / 19

Introduction ◮ Hash tables are fundamental data structures A Parallel Compact Hash Table October 3, 2011 3 / 19

Introduction ◮ Hash tables are fundamental data structures ◮ Compact hash tables: memory efficient hash tables A Parallel Compact Hash Table October 3, 2011 3 / 19

Introduction ◮ Hash tables are fundamental data structures ◮ Compact hash tables: memory efficient hash tables ◮ Useful in i.e. Model checking, planning, BDDs, Tree tables A Parallel Compact Hash Table October 3, 2011 3 / 19

Introduction ◮ Hash tables are fundamental data structures ◮ Compact hash tables: memory efficient hash tables ◮ Useful in i.e. Model checking, planning, BDDs, Tree tables ◮ Problem: No concurrent implementation of concurrent hash tables A Parallel Compact Hash Table October 3, 2011 3 / 19

Introduction ◮ Hash tables are fundamental data structures ◮ Compact hash tables: memory efficient hash tables ◮ Useful in i.e. Model checking, planning, BDDs, Tree tables ◮ Problem: No concurrent implementation of concurrent hash tables ◮ Our contribution: A scalable lockless algorithm for compact hashing A Parallel Compact Hash Table October 3, 2011 3 / 19

Goals ◮ Parallel compact hash table ◮ Scalable ◮ Fast: lockless ◮ Memory efficient: no pointers (otherwise we lose the benefits from compact hashing) ◮ Focus on findOrPut ◮ Already sufficient Model checking (monotonic growing dataset) ◮ subsumes individual find and put operations A Parallel Compact Hash Table October 3, 2011 4 / 19

Overview Research Motivation Background Contribution A Parallel Compact Hash Table October 3, 2011 5 / 19

Hashing Revisited ◮ A hash table stores a subset of a key universe U into an table T of buckets typically | U | ≫ | T | ◮ Multiple keys can be mapped upon 1 bucket ◮ The full key is stored in T to resolve collisions ◮ Several possible collision resolution algorithms, i.e. linear probing A Parallel Compact Hash Table October 3, 2011 6 / 19

Hashing Revisited - Example keys buckets 000 001 Lisa Smith 521-8976 John Smith 002 : : : Lisa Smith 151 152 John Smith 521-1234 Sam Doe 153 Sandra Dee 521-9655 154 T ed Baker 418-4165 Sandra Dee 155 : : : T ed Baker 253 254 Sam Doe 521-5030 255 Figure: Example of an open addressing hash table. A Parallel Compact Hash Table October 3, 2011 7 / 19

Introduction Into Compact Hash Tables ◮ If however | U | ≤ | T | , we only need a bit array! (and a perfect hash function) ◮ What if | U | just slightly bigger than | T | ? Cleary Tables: 1. Maintain order in T 2. Add three bits to buckets in T A Parallel Compact Hash Table October 3, 2011 8 / 19

Introduction Into BLP Let K be the set of possible keys and h the hash function which computes the indexes. h : K → { 0 .. M − 1 } with the property K 1 , K 2 ∈ K | K 1 ≤ L 2 iff h ( K 1 ) ≤ h ( K 2 ) ◮ All keys are stored in ascending order. ◮ There can not be empty locations between a keys original hash location and its actual storage position. ◮ All keys sharing the same initial hash location form one continuous group . ◮ Groups can grow together forming clusters of groups. ◮ Bidirectional linear probing algorithm (probing possible in both directions) A Parallel Compact Hash Table October 3, 2011 9 / 19

Introduction Into BLP - Insert Example Inserting k into table T in 5 steps: 1. Determine index: i ← h ( k ) 2. Determine probing direction T [ h ( k )] > k ? right : left 3. Search empty bucket 4. Insert K into empty bucket 5. Swap bucket into correct place A Parallel Compact Hash Table October 3, 2011 10 / 19

Cleary Table Cleary administration bits: ◮ Virgin Set upon a bucket if its location is the initial hash location for some key in the tables ◮ Change Set at the beginning of a group with the same initial hash location ◮ Occupied Set if the bucket contains a key A Parallel Compact Hash Table October 3, 2011 11 / 19

Cleary Table - Example Figure: Example of a partially filled Cleary table with 4 groups. A Parallel Compact Hash Table October 3, 2011 12 / 19

Overview Research Motivation Background Contribution A Parallel Compact Hash Table October 3, 2011 13 / 19

Requirements for Parallelizing We need a write-exclusive locking mechanism that ◮ Scales well ◮ Is memory efficient A Parallel Compact Hash Table October 3, 2011 14 / 19

Locking Mechanism Properties: ◮ 1 bit per bucket A Parallel Compact Hash Table October 3, 2011 15 / 19

Locking Mechanism Properties: ◮ 1 bit per bucket ◮ CAS(a,b,c) - Compare-and-Swap ( if a == b then a ← c ) A Parallel Compact Hash Table October 3, 2011 15 / 19

Locking Mechanism Properties: ◮ 1 bit per bucket ◮ CAS(a,b,c) - Compare-and-Swap ( if a == b then a ← c ) Locking steps: 1. Search for both left and right bucket of cluster A Parallel Compact Hash Table October 3, 2011 15 / 19

Locking Mechanism Properties: ◮ 1 bit per bucket ◮ CAS(a,b,c) - Compare-and-Swap ( if a == b then a ← c ) Locking steps: 1. Search for both left and right bucket of cluster 2. Lock these buckets A Parallel Compact Hash Table October 3, 2011 15 / 19

Locking Mechanism Properties: ◮ 1 bit per bucket ◮ CAS(a,b,c) - Compare-and-Swap ( if a == b then a ← c ) Locking steps: 1. Search for both left and right bucket of cluster 2. Lock these buckets 3. If one of these locks fails → unlock and start over A Parallel Compact Hash Table October 3, 2011 15 / 19

Locking Mechanism Properties: ◮ 1 bit per bucket ◮ CAS(a,b,c) - Compare-and-Swap ( if a == b then a ← c ) Locking steps: 1. Search for both left and right bucket of cluster 2. Lock these buckets 3. If one of these locks fails → unlock and start over 4. Perform exclusive actions (read, write) A Parallel Compact Hash Table October 3, 2011 15 / 19

Dynamic Region Based Locking 1: left ← CL - LEFT ( h ) 2: right ← CL - RIGHT ( h ) 3: if ¬ TRY - LOCK ( T [ left ]) then 4: RESTART 5: if ¬ TRY - LOCK ( T [ right ]) then UNLOCK ( T [ left ]) 6: 7: RESTART 8: if FIND ( k ) then ⊲ exclusive read UNLOCK ( T [ left ] , T [ right ] ) 9: return FOUND 10: 11: PUT ( k ) ⊲ exclusive write 12: UNLOCK ( T [ left ] , T [ right ] ) A Parallel Compact Hash Table October 3, 2011 16 / 19

Benchmarks - Speedup 12.0 LHT 0:1 LHT 3:1 11.0 LHT 9:1 RBL 0:1 10.0 RBL 3:1 RBL 9:1 9.0 BLP 0:1 BLP 3:1 8.0 BLP 9:1 7.0 PCT 0:1 Speedup PCT 3:1 PCT 9:1 6.0 Ideal Speedup 5.0 4.0 3.0 2.0 1.0 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Cores Figure: Speedups of BLP , RBL, LHT and PCT with r/w ratios 0:1, 3:1 and 9:1 A Parallel Compact Hash Table October 3, 2011 17 / 19

Benchmarks - Runtime 200.0 LHT 0:1 LHT 3:1 180.0 LHT 9:1 RBL 0:1 RBL 3:1 RBL 9:1 160.0 BLP 0:1 BLP 3:1 140.0 normalized runtime BLP 9:1 PCT 0:1 PCT 3:1 PCT 9:1 120.0 100.0 80.0 60.0 40.0 20.0 0.0 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100% load factor Figure: 16-core runtimes of BLP , RBL, LHT and PCT with r/w ratios 0:1, 3:1 and 9:1. A Parallel Compact Hash Table October 3, 2011 18 / 19

Results ◮ PCT performs very good with only inserts, ◮ PCT’s performance drops when the load-factor becomes above the 85% ◮ With a high amount of reads ¿ (9:1) BLP eventually becomes faster than LHT ◮ Region based locking with OS-locks is very slow as can be seen in RBL ◮ scalability of both PCL and BLP is good. ◮ r/w ratio: r/w exclusion on clusters takes a toll. there is room for improvement if look at the higher load factors (when clusters are large) A Parallel Compact Hash Table October 3, 2011 19 / 19

Conclusion ◮ We have realized parallel cleary with high performance and scalability up to load-factors of 90% Since the compression ratio of compact hash tables can be high, this is acceptable ◮ Future work: Allow for concurrent reads with cleary to improve scalability of Cleary even more A Parallel Compact Hash Table October 3, 2011 20 / 19