Algorithm Engineering Parallele Algorithmen Stefan Edelkamp.

Präsentation zum Thema: "Algorithm Engineering Parallele Algorithmen Stefan Edelkamp."—  Präsentation transkript:

1 Algorithm Engineering Parallele Algorithmen Stefan Edelkamp

2 Übersicht Parallele Externe Suche Parallele Verspätete Duplikatselimination Parallele Expansion Verteilte Sortierung Parallele Strukturierte Duplikatselimination Disjunkte Duplikatserkennungsbereiche Schlöser Parallele Algorithmen Matrix-Multiplikation List Ranking Euler Tour

3 Verteilte Suche Distributed setting provides more space. Experiments show that internal time dominates I/O.

4 Exploiting Independence Since each state in a Bucket is independent of the other – they can be expanded in parallel. Duplicates removal can be distributed on different processors. Bulk (Streamed) transfers much better than single ones.

5 Distributed Queue for Parallel Best- First Search P0 P1 P2 TOP Beware of the Mutual Exclusion Problem!!!

6 Multiple Processors - Multiple Disks Variant Sorted buffers w.r.t the hash val Sorted Files P1 P2 P3P4 Divide w.r.t the hash ranges Sorted buffers from every processor Sorted File h 0 ….. h k-1 h k ….. h l-1

7 Parallel External A*

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10 Distributed Heuristic Evaluation Assume one child processor for each tile one master processor B3B3 B1B1 B2B2 B8B8 B4B4 B5B5 B6B6 B7B7 B9B9 B 10 B 11 B 12 B 13 B 14 B 15 B0B0 B3B3 B1B1 B2B2 B8B8 B4B4 B5B5 B6B6 B7B7 B9B9 B 10 B 11 B 12 B 13 B 14 B 15 B0B0

11 Distributed Pattern Database Search Only pattern databases that include the client tile need to be loaded on the client Because multiple tiles in pattern, from birds eye PDB loaded multiple times In 15-Puzzle with corner and fringe PDB this saves RAM in the order of factor 2 on each machine, compared to loading all In 36-Puzzle with 6-tile pattern databases this saves RAM in the order of factor 6 on each machine, compared to loading all Extends to additive pattern databases

12 Distributed Heuristic Evaluation

13 Same bottleneck in external-memory search Bottleneck: Duplicate detection Duplicate paths cause parallelization overhead A C D B BCDDDD Internal memory External memory vs. fast slow A

14 Disjoint duplicate-detection scopes B1B1 B0B0 B4B4 B0B0 B3B3 B1B1 B2B2 B8B8 B4B4 B5B5 B6B6 B7B7 B9B9 B 10 B 11 B 12 B 13 B 14 B 15 B0B0 B1B1 B4B4 B3B3 B2B2 B7B7 B2B2 B3B3 B7B7 B 12 B8B8 B 13 B 15 B 14 B 11 B8B8 B 12 B 13 B 11 B 15 B 14

15 Finding disjoint duplicate-detection scopes B1B1 B0B0 B4B4 0000 0 0 000 00 1 0000 0 1 1 0 2 1 B2B2 B3B3 B7B7 0 1 0 B8B8 B 12 B 13 B 11 B 15 B 14 1 2 2 01 2 2 2 2 1 2 2 2 2 2 0 1 1 1 0 1 0 2 3 3 2 B1B1 B5B5 B6B6 B4B4 B9B9 2 3 3 4 3 3

16 Implementation of Parallel SDD Hierarchical organization of hash tables One hash table for each abstract node Top-level hash func. = state-space projection func. Shared-memory management Minimum memory-allocation size m Memory wasted is bounded by O(m #processors) External-memory version I/O-efficient order of node expansions I/O-efficient replacement strategy Benötigt nur ein Mutex Schloss B3B3 B1B1 B2B2 B8B8 B4B4 B5B5 B6B6 B7B7 B9B9 B 10 B 11 B 12 B 13 B 14 B 15 B0B0

17 Parallelle Matrix- Multiplication

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19 Parallele Matrix Multiplication

20 Exklusives Schreiben

21 Parallele Kopien

22 Fazit Matrix Multiplication

23 Paralleles List Ranking

24 List Ranking

25 Erster Algorithmus

26 Prinzip

27 Komplexität

28 Verbesserungen

29 Strategie

30 Unabhängige Mengen

31 2-Färbung

32 Reduktion

33 Restauration

34 Beispiel

35 Variablen

36 Beispiel (ctd.)

37 Pseudo Code

38 Nächster Schritt

39 Analyse

40 Backup

41 Algo

42

43 Speicher

44 Analyse

45 Ausblick: Randomisiert in O(n) whp?

46 Probleme mit DFS

47 Idee Euler Tour

48 Parallel DFS

49 DFS Nummern

50 Allgemein

51

52

53 Beispiel

54 Ein Zyklus oder mehrere?

55 Korrektheit

56

57 Beispiel

58 Konstruktion Euler Tour

59 Fazit Euler Touren

60 GPU Architektur

61 Effektivität

62 Hierarchischer Speicher

63 Hash-based Partitioning

64 BFS

65 Kernel Functions