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We present a novel approach to parallel materialisation (i.e.,

fixpoint computation) of datalog programs in centralised,

main-memory, multi-core RDF systems. Our approach comprises an algorithm that evenly distributes the workload to cores, and an RDF indexing data structure that supports efficient, ‘mostly’ lock-free parallel updates. Our empirical evaluation shows that our approach parallelises computation very well: with 16 physical cores, materialisation can be up to 13.9 times faster than with just one core.

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- 1. PARALLEL DATALOG REASONING IN RDFOX Boris Motik, Yavor Nenov, Robert Piro, Ian Horrocks, Dan Olteanu University of Oxford September 25, 2014
- 2. TABLE OF CONTENTS 1 INTRODUCTION 2 OUR APPROACH TO PARALLEL MATERIALISATION 3 EVALUATION 4 CONCLUSION Motik et al. Parallel Datalog Reasoning in RDFox 0/9
- 3. Introduction TABLE OF CONTENTS 1 INTRODUCTION 2 OUR APPROACH TO PARALLEL MATERIALISATION 3 EVALUATION 4 CONCLUSION Motik et al. Parallel Datalog Reasoning in RDFox 0/9
- 4. Introduction CURRENT TRENDS IN KNOWLEDGE/DATABASE SYSTEMS Materialisation is computationally intensive ) natural to parallelise mid-range laptops have 4 cores, servers with 16 cores are routine Price of RAM keeps falling 128 GB is routine, systems with 1 TB are emerging in-memory databases: SAP’s HANA, Oracle’s TimesTen, YarcData’s Urika Motik et al. Parallel Datalog Reasoning in RDFox 1/9
- 5. Introduction RDFOX SUMMARY RDFox: a new RDF store and reasoner http://www.cs.ox.ac.uk/isg/tools/RDFox/ store data in RAM effectively use modern multi-core architectures Core focus: materialisation reasoning (recursive) datalog rules e.g., hx; rdf :type; yi ^ hy; rdfs:subClassOf ; zi ! hx; rdf :type; zi handle OWL 2 RL and the Semantic Web Rule Language (SWRL) explicitly store all implied triples so that queries can be evaluated directly used in a number of systems: Oracle’s database, OWLIM, WebPIE Used in projects for reasoning beyond OWL 2 RL ‘combined approach’ for reasoning with OWL 2 EL PAGOaA reasoner for OWL 2 DL comdining RDFox with HermiT Motik et al. Parallel Datalog Reasoning in RDFox 2/9
- 6. Our Approach to Parallel Materialisation TABLE OF CONTENTS 1 INTRODUCTION 2 OUR APPROACH TO PARALLEL MATERIALISATION 3 EVALUATION 4 CONCLUSION Motik et al. Parallel Datalog Reasoning in RDFox 2/9
- 7. Our Approach to Parallel Materialisation EXISTING APPROACHES TO PARALLEL MATERIALISATION Interquery parallelism: run independent rules in parallel degree of parallelism limited by the number of independent rules ) does not distribute workload to cores evenly Intraquery parallelism: partition rule instantiations to N threads e.g., constrain the body of rules evaluated by thread i to (x mod N = i) ) static partitioning may not distribute workload well due to data skew ) dynamic partitioning may incur an overhead due to load balancing Goal: distribute workload to threads evenly and with minimum overhead Motik et al. Parallel Datalog Reasoning in RDFox 3/9
- 8. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) A(a) R(c,f) R(c,g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 9. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM ) R(a,b) R(a,c) R(b,d) R(b,e) A(a) R(c,f) R(c,g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: A(a) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 10. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) ) R(a,c) R(b,d) R(b,e) A(a) R(c,f) R(c,g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: A(a) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 11. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) ) R(b,d) R(b,e) A(a) R(c,f) R(c,g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: A(b) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 12. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) ) R(b,e) A(a) R(c,f) R(c,g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: A(b) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 13. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) ) A(a) R(c,f) R(c,g) A(b) A(c) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: R(a,y) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 14. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) A(a) ) R(c,f) R(c,g) A(b) A(c) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: A(c) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 15. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) A(a) R(c,f) ) R(c,g) A(b) A(c) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: A(c) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 16. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) A(a) R(c,f) R(c,g) ) A(b) A(c) A(d) A(e) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: R(b,y) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 17. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) A(a) R(c,f) R(c,g) A(b) ) A(c) A(d) A(e) A(f) A(g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: R(c,y) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 18. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) A(a) R(c,f) R(c,g) A(b) A(c) ) A(d) A(e) A(f) A(g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: R(d,y) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 19. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) A(a) R(c,f) R(c,g) A(b) A(c) A(d) ) A(e) A(f) A(g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: R(e,y) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 20. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) A(a) R(c,f) R(c,g) A(b) A(c) A(d) A(e) ) A(f) A(g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: R(f,y) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 21. Our Approach to Parallel Materialisation SOLUTION PART I: ALGORITHM R(a,b) R(a,c) R(b,d) R(b,e) A(a) R(c,f) R(c,g) A(b) A(c) A(d) A(e) A(f) ) A(g) A(x) ^ R(x; y) ! A(y) For each fact: match the fact to all body atoms to obtain subqueries evaluate subqueries w.r.t. all previous facts add results to the table Current subquery: R(g,y) Motik et al. Parallel Datalog Reasoning in RDFox 4/9
- 22. Our Approach to Parallel Materialisation PARALLELISING COMPUTATION Each thread extracts facts and evaluates subqueries independently The number of subqueries is determined by the number of facts ensures in practice that threads are equally loaded Requires no thread synchronisation ) We partition rule instances dynamically and with little overhead EXAMPLE WHEN PARALLELISATION FAILS A(x) ^ R(x; y) ! A(y) R(a; b); R(b; c); R(c; d); R(d; e); A(a) Motik et al. Parallel Datalog Reasoning in RDFox 5/9
- 23. Our Approach to Parallel Materialisation PARALLELISING COMPUTATION Each thread extracts facts and evaluates subqueries independently The number of subqueries is determined by the number of facts ensures in practice that threads are equally loaded Requires no thread synchronisation ) We partition rule instances dynamically and with little overhead EXAMPLE WHEN PARALLELISATION FAILS A(x) ^ R(x; y) ! A(y) R(a; b); R(b; c); R(c; d); R(d; e); A(a); A(b) Motik et al. Parallel Datalog Reasoning in RDFox 5/9
- 24. Our Approach to Parallel Materialisation PARALLELISING COMPUTATION Each thread extracts facts and evaluates subqueries independently The number of subqueries is determined by the number of facts ensures in practice that threads are equally loaded Requires no thread synchronisation ) We partition rule instances dynamically and with little overhead EXAMPLE WHEN PARALLELISATION FAILS A(x) ^ R(x; y) ! A(y) R(a; b); R(b; c); R(c; d); R(d; e); A(a); A(b); A(c) Motik et al. Parallel Datalog Reasoning in RDFox 5/9
- 25. Our Approach to Parallel Materialisation PARALLELISING COMPUTATION Each thread extracts facts and evaluates subqueries independently The number of subqueries is determined by the number of facts ensures in practice that threads are equally loaded Requires no thread synchronisation ) We partition rule instances dynamically and with little overhead EXAMPLE WHEN PARALLELISATION FAILS A(x) ^ R(x; y) ! A(y) R(a; b); R(b; c); R(c; d); R(d; e); A(a); A(b); A(c); A(d) Motik et al. Parallel Datalog Reasoning in RDFox 5/9
- 26. Our Approach to Parallel Materialisation PARALLELISING COMPUTATION Each thread extracts facts and evaluates subqueries independently The number of subqueries is determined by the number of facts ensures in practice that threads are equally loaded Requires no thread synchronisation ) We partition rule instances dynamically and with little overhead EXAMPLE WHEN PARALLELISATION FAILS A(x) ^ R(x; y) ! A(y) R(a; b); R(b; c); R(c; d); R(d; e); A(a); A(b); A(c); A(d); A(e) Motik et al. Parallel Datalog Reasoning in RDFox 5/9
- 27. Our Approach to Parallel Materialisation SOLUTION PART II: INDEXING RDF DATA IN MAIN MEMORY The critically algorithm depends on: matching atoms ht1; t2; t3i with ti a constant or variable continuous concurrent updates Our RDF storage data structure: hash-based indexes ) naturally parallel data structure ‘mostly’ lock-free: at least one thread makes progress at most of the time compare: if a thread acquire a lock and dies, other threads are blocked main benefit: performance is less susceptible to scheduling decisions Main technical challenge: reduce thread interference when A writes to a location cached by B, the cache of B is invalidated our updates ensure that threads (typically) write to different locations Motik et al. Parallel Datalog Reasoning in RDFox 6/9
- 28. Evaluation TABLE OF CONTENTS 1 INTRODUCTION 2 OUR APPROACH TO PARALLEL MATERIALISATION 3 EVALUATION 4 CONCLUSION Motik et al. Parallel Datalog Reasoning in RDFox 6/9
- 29. Evaluation CONCURRENCY OVERHEAD AND PARALLELISATION SPEEDUP RDFox: an RDF store developed at Oxford University http://www.cs.ox.ac.uk/isg/tools/RDFox/ 8 16 24 32 20 18 16 14 12 10 8 6 4 2 ClarosL ClarosLE DBpediaL DBpediaLE LUBML01K LUBMU01K 8 16 24 32 20 18 16 14 12 10 8 6 4 2 UOBML01K UOBMU010 LUBMLE 01K LUBML05K LUBMLE 05K LUBMU05K Small concurrency overhead; parallelisation pays off already with two threads Speedup continues to increase after we exhaust all physical cores ) hyperthreading and parallelism can compensate CPU cache misses Motik et al. Parallel Datalog Reasoning in RDFox 7/9
- 30. 32 127 19.5 285 17.5 24 6.6 602 15.1 7 10.1 71 13.4 10 13.4 Mem Mem Mem 168 16.3 31 17.1 Evaluation Seq. imp. 61 57 331 335 421 408 410 2610 2587 2643 6 798 Par. imp. 58 -4.9% 58 1.7% COMPARISON 334 0.9% 367 9.5% WITH 415 1.4% 415 THE 1.7% STATE 415 1.2% 2710 OF 3.8% THE 3553 ART 37% 2733 3.4% 6 0.0% 783 -1.9% Triples 95.5M 555.1M 118.3M 1529.7M 182.4M 332.6M 219.0M 911.2M 1661.0M 1094.0M 35.6M 429.6M Memory 4.2GB 18.0GB 6.1GB 51.9GB 9.3GB 13.8GB 11.1GB 49.0GB 75.5GB 53.3GB 1.1GB 20.2GB Active 93.3% 98.8% 28.1% 94.5% 66.5% 90.3% 85.3% 66.5% 90.3% 85.3% 99.7% 99.1% (b) Comparison of SysX with DBRDF and OWLIM-Lite SysX PG-VP MDB-VP PG-TT MDB-TT OWLIM-Lite Import Materialise Import Materialise Import Materialise Import Import Import Materialise T B/t T B/t T B/t T B/t T B/t T B/t T B/t T B/t T B/t T B/t ClarosL 48 89 2062 60 1138 165 25026 97 883 58 Mem 1174 217 896 94 300 54 14293 28 ClarosLE 4218 44 Mem Mem Time DBpediaL 143 67 Mem 354 49 274 69 5844 148 15499 51 5968 174 4492 92 1735 171 14855 164 DBpediaLE 9538 49 Mem Mem Time LUBML01K 332 74 71 65 7736 144 948 127 6136 56 27 41 7947 187 5606 104 2409 40 316 36 LUBMLE 01K 765 54 15632 112 Mem Time LUBMU01K 113 67 Time 138 44 Time UOBMU010 5 68 2501 43 116 154 Time 96 50 Mem 120 203 96 85 32 69 11311 24 UOBML01K 632 64 467 63 13864 119 6708 107 11063 41 358 33 14901 176 10892 101 4778 38 Time Figure 2: Results of our Empirical Evaluation DBRDF: an implementation using RDBMS and known techniques PostgreSQL (row store) or MonetDB (column store) as underlying engine vertical partitioning (VP) or triple table (TT) storage model averages over three runs. OWLIM-Lite materialisation and import, so we loaded each the test datalog program and once with subtracted the two times; Ontotext con-firmed OWLIM-Lite: a commercial RDF store by OntoText good materialisation time estimate. Table (a) in Figure 2 show the speedup number of used threads. The middle part sequential and parallel import times, slowdown for the parallel version. The shows the number of triples, the mem-ory speedup as s(1) = 1/(1 − p(1)); assuming that p(1) = p(32), we get s(1) between 8.3 and 50. With 32 threads we thus already approach this maximum, which ex-plains the flattening of the curves in Figure 2. Table (b) in Figure 2 compares SysX with DBRDF on PostgreSQL (PG) and MonetDB (MDB) with VP or TT scheme, and with OWLIM-Lite. Columns T show the times in seconds, and columns B/t show the number of bytes per triple. Import in DBRDF is about 20 times slower than in SysX; we found out that half of the import time is used in Motik et al. Parallel Datalog Reasoning in RDFox 8/9
- 31. Conclusion TABLE OF CONTENTS 1 INTRODUCTION 2 OUR APPROACH TO PARALLEL MATERIALISATION 3 EVALUATION 4 CONCLUSION Motik et al. Parallel Datalog Reasoning in RDFox 8/9
- 32. Conclusion RESEARCH DIRECTIONS Under development/already finished: Deal with owl:sameAs via rewriting Incremental deletions/additions Add a data/query/reasoning distribution layer Future work: Investigate potential for data compression Improve join cardinality estimation Improve query planning Motik et al. Parallel Datalog Reasoning in RDFox 9/9

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