Overview Problem Statement Related Work KLEE The Histogram Bloom Structure Candidate Filtering Evaluation Conclusion / Future Work

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Sebastian Michel Max-Planck Institute for Informatics Saarbrücken,

de KLEE: Approximate Distributed Top-k Query Algorithms Peter

Saarbrücken, Germany weikum@mpi-inf.mpg.

1 Sebastian Michel Max-Planck Institute for Informatics Saarbrücken, Germany KLEE: Approximate Distributed Top-k Query Algorithms Peter Triantafillou RACTI / Univ. of Patras Rio, Greece peter@ceid.upatras.gr Gerhard Weikum Max-Planck Institute for Informatics Saarbrücken, Germany weikum@mpi-inf.mpg.de Max-Planck-Institut Informatik University of Patras NetCInS Lab Overview Problem Statement Related Work KLEE The Histogram Bloom Structure Candidate Filtering Evaluation Conclusion / Future Work HDMS 25, Athens 2

2 Computational Model distributed aggregation queries: Query with m terms with index lists spread across m peers P... Pm P2 P5 P P3 P4 Applications: Internet traffic monitoring Sensor networks P2P Web search HDMS 25, Athens 3 Problem Statement Query initiator P serves as per-query coordinator P t d78.9 d23.8 d.8 d.7 d88.2 P P2 t 2 d64.8 d23.6 d.6 d.2 d78. P3 t 3 d.7 d78.5 d64.4 d99.2 d34. Consider network consumption per peer load latency (query response time) network I/O processing HDMS 25, Athens 4 2

3 Related Work Existing Methods: Distributed NRA/TA: NRA/TA (Fagin et al. `99/ 3, Güntzer et al. `, Nepal et al. `99) with batched access TPUT (Cao/Wang 24): ) fetch k best entries (d, s j ) from each of P... Pm and aggregate ( j=..m s j (d)) at P 2) ask each of P... Pm for all entries with s j > and aggregate results at P 3) fetch missing s for all candidates by random lookups at P... Pm + DNRA aims to minimize per-peer work - DTA/DNRA incur many messages + TPUT guarantees fixed number of message rounds - TPUT incurs high per-peer load and net BW HDMS 25, Athens 5 TPUT Coordinator Peer P current top-kcandidate set Peer Pi candidates top k Retrieve missing s Peer Pj candidates top k Retrieve missing s... Index List... Index List HDMS 25, Athens 6 3

4 KLEE: Key Ideas if mink / m is small TPUT retrieves a lot of data in Phase 2 high network traffic random accesses high per-peer load KLEE: Different philosophy: approximate answers! Efficiency: Reduces (docid, )-pair transfers no random accesses Two pillars: The HistogramBlooms structure The Candidate List Filter structure HDMS 25, Athens 7 KLEE 3/4: The KLEE Algorithms. Exploration Step: to get a better approximation of min-k threshold 2. Optimization Step: decide: 3 or 4 phases? 3. Candidate Filtering: a docid is a good candidate if high-d in many peers. 4. Candidate Retrieval: get all good docid candidates. HDMS 25, Athens 8 4

5 Histogram Bloom Structure Each peer pre-computes for each index list: an equi-width histogram #docs + Bloom filter for each cell + average per cell + upper/lower increase the mink / m threshold HDMS 25, Athens 9 Bloom Filter bit array of size m k hash functions h i : docid_space {,..,m} insert n docs by hashing the ids and settings the corresponding bits Membership Queries: document is in the Bloom Filter if the corresponding bits are set kn / m probability of false positives (pfp) pfp = ( e ) tradeoff accuracy vs. efficiency k HDMS 25, Athens 5

6 Exploration and Candidate Retrieval Coordinator Peer P current top-kcandidate set Peer Pi candidates top k c cells b bits Histogram Peer Pj candidates top k c cells b bits Histogram... Index List... Index List HDMS 25, Athens Candidate List Filter Matrix Goal: filter out unpromising candidate documents in step 2 estimate the max number of docs that are above the mink / m threshold number of documents threshold send this number and the threshold to the cohort peers HDMS 25, Athens 2 6

7 Candidate List Filter Matrix (2) Each cohort returns a Bloom Filter that contains all docs above the mink / m threshold Candidate List Filter Matrix (CLFM) Select all columns with at least R bits set HDMS 25, Athens 3 Coordinator Peer P KLEE Candidate Set Reduction current top-k candidate set candidate filter matrix x x x Peer Pi top k Peer Pj candidates... Index List HDMS 25, Athens 4 7

8 Coordinator Peer P KLEE Candidate Retrieval current top-k candidate set candidate filter matrix x x x Peer Pi top k Peer Pj candidates... Index List early stopping point HDMS 25, Athens 5 Enhanced Filtering BF represenation can be improved (d,.9) (d2,.6) (d5,.5) (d3,.3) (d4,.25) (d7,.8) (d9,.7) Cell Cell 2 Cell 3 d cell and d2 cell but s s2 =.3! Send byte-array with cell-numbers instead of bits Select columns with Sum over upper-bounds > min-k HDMS 25, Athens 6 8

9 Architecture/Testbed 2 KLEE Algorithmic Framework 4 3 open() get(k) getabove()... getwithbf(..) open() next() close() Extended IndexLists with BloomFilters, Histograms, and Batched Access SQL B+ Index Index Lists Oracle DB HDMS 25, Athens 7 Evaluation: Benchmarks GOV: TREC.GOV collection + 5 TREC-23 Web queries, e.g. juvenile delinquency XGOV: TREC.GOV collection + 5 manually expanded queries, e.g. juvenile delinquency youth minor crime law jurisdiction offense prevention IMDB: Movie Database, queries like actor = John Wayne; genre =western Synthetic Distribution (Zipf, different skewness): GOV collection but with synthetic s Synthetic Distribution + Synthetic Correlation: index lists HDMS 25, Athens 8 9

10 Evaluation: Metrics Relative recall w.r.t. to the actual results Score error Bandwidth consumption Rank distance Number of RA and number of SA Query response time - network cost (5ms RTT, 8Kb/s data transfer rate) - local I/O cost (8ms rotation latency + 8MB/s transfer delay) - processing cost HDMS 25, Athens 9 DTA: Evaluated Algorithms batched distributed threshold algorithm, batch size k. TPUT X-TPUT: approximate TPUT. No random accesses. KLEE-3 KLEE-4 C = % of the mass HDMS 25, Athens 2

11 Synthetic Score Benchmarks Zipf-GOV Total Total Average c=% # of Bytes Time in ms Recall DTA 7,752,769 3,532,8 TPUT 53,494,93 576,73 X-TPUT 53,,252 44,99.99 KLEE 3 49,86, ,93.97 KLEE 4 25,57,92 6, Zipf-XGOV Total Total Average c=% # of Bytes Time in ms Recall DTA 67,9,26 39,582,682 TPUT 377,928,88,599,58 X-TPUT 377,97,644,52,22.98 KLEE 3 287,294,82,89,89.9 KLEE 4 65,77,87 375,77.92 Bandwidth in Bytes 2.5E+7 2.E+7.5E+7.E+7 5.E+6.E+ Zipf-XGOV, c=%, θ=.7 DTA TPUT X-TPUT KLEE 3 KLEE Number of Query Terms θ =.7 HDMS 25, Athens 2 Synthetic Correlation Benchmark Overlap+Zipf Total Total Average c=% Ω = 3% # of Bytes Time in ms Recall DTA, ,42 TPUT 9,5,94 29,27 X-TPUT 9,5,94 28,335 KLEE 3 3,678,78 2,97.92 KLEE 4,92,74 6,546.9 randomly insert top k documents from list i in the top Ω documents of list j Ω Bandwidth in Bytes,, 9,, 8,, 7,, 6,, 5,, 4,, 3,, 2,,,, Overlap, c=%, θ=.7 DTA TPUT X-TPUT KLEE 3 KLEE Ω in % HDMS 25, Athens 22

12 GOV / XGOV GOV Total Total Average c=% # of Bytes Time in ms Recall DTA,72,446 9,259 TPUT,55,29 85,49 X-TPUT 597,99 3, KLEE 3 722,664 28,39.9 KLEE 4 44,868 39,564.9 XGOV Total Total Average c=% # of Bytes Time in ms Recall DTA 92,587,264 3,74,677 TPUT 7,44,884 2,346,882 X-TPUT 9,236,84 96,53.9 KLEE 3 6,69,92 88,27.83 KLEE 4 7,92,774 56, , GOV, c=% 6,, XGOV, c=% Bandwidth in Bytes 2,, 8, 6, 4, 2, DTA TPUT X-TPUT KLEE 3 KLEE Number of Query Terms Bandwidth in Bytes 5,, 4,, 3,, 2,,,, TA TPUT X-TPUT KLEE 3 KLEE Number of Query Terms HDMS 25, Athens 23 Conclusion / Future Work Conclusion KLEE: approximate top-k algorithms for wide-area networks significant performance benefits can be enjoyed, at only small penalties in result quality flexible framework for top-k algorithms, allowing for trading-off efficiency versus result quality and bandwidth savings versus the number of communication phases. various fine-tuning parameters Future Work Reasoning about parameter values Consider moving coordinator HDMS 25, Athens 24 2

13 Thanks for your attention! Questions? Comments? HDMS 25, Athens 25 3

KLEE: A Framework for Distributed Top-k Query Algorithms

KLEE: A Framework for Distributed Top-k Query Algorithms Sebastian Michel Max-Planck Institute for Informatics Saarbrücken, Germany smichel@mpi-inf.mpg.de Peter Triantafillou RACTI / Univ. of Patras Rio,