Bi-Temporal Relation Model. Zonr Dec 26, 2007

Transcription

1 Bi-Temporal Relation Model Zonr Dec 26, 2007

2 The TSQL2 Data Model Christian S. Jensen Richard T. Snodgrass Michael D. Soo (1995)

3 Temporal Database Papers [VA 96] [Kline 93]

4 What is Temporal Database?

5 Database Built-in Time Aspects [Wikipedia 07]

6 Daunting Task [Soo 91] [SS 88] [McKenzie 86] [BADW 82]

7 WHY?

8 Transaction-Time v.s. Valid-Time

9 First Normal Form

10 Data Representation

11 Valid time Concern the time when a fact is true in modeled reality Transaction time Concern the time the fact was present in database Event

12 Name Course Time Op Bill English 423 Insert Bill English 427 Modify George English 438 Insert Bill English 452 Insert George Math 487 Insert George Math 495 Delete [Jensen 91]

13 1NF Timestamp of tuples are start and end time ex. Relation model introduced in Chapter 2 Cause redundancy

14 Course Instructor Duration Intro. to Computer Sam : 1973, 1975) Intro. to Computer Sam : 1977, 1979) Intro. to Computer Sam : 1985, 1995) Intro. to Computer Sam : 1998, 2004) Computer Prog. Bob : 1973, 1975) Computer Prog. Bob : 1978, 1986) Computer Prog. Bob : 1989, 1995)

15 Non-1NF Timestamp of tuples are set of intervals ex. Relation model introduced in Chapter 1 Cannot fit existing relational storage structure

16 Course Instructor Lifespan Intro. to Computer Computer Prog. 1973, Sam 1977, Sam 1985, Sam 1998, Sam 1973, Bob 1978, Bob 1989, Bob { [1973, 1975], [1977, 1979], [1985, 1995], [1998, 2004] } { [1973, 1975], [1978, 1986], [1989, 1995] }

17 We want to focus on... Data Representation Data Storage Query Evaluation Compatible Simultaneously focus may cause complicated data model

18 Daunting Task [Soo 91] [SS 88] [McKenzie 86] [BADW 82]

19 Approach

20 Introduce a new data model

21 Simple but enough powerful

22 Concept

23 Introduce a new conceptual data model

24 Transform Concept Represent

25 Transform Concept Represent

26 Where may be our entry point?

27

28 Valid time and Transaction time are COMPLETELY different two things Semantic Orthogonal

29 Valid Yes Valid Time Temporal Bi-Temporal No Yes Transaction Snapshot Trans. Time Temporal No

30 Valid Tansel 86 Sarda 90 Yes Snodgrass 87 Gadia 92 Gadia 88 No Yes Transaction Stonebraker 87 Jensen 91 No Kimball 78

31 Which dimension we choose making powerful enough?

32 Valid Tansel 86 Sarda 90 Yes Snodgrass 87 Gadia 92 Gadia 88 Here No Yes Transaction Stonebraker 87 Jensen 91 No Kimball 78

33 Bitemporal Conceptual Data Model

34 Bi-Temporal Conceptual Model The smallest time unit we call it chronon

35 DVT = { t1, t2, t3... tk } D TT = { t 1, t 2, t 3... t k } { UC } UC, Until Change DA = { A1, A2, A3... Ak } DD = { D1, D2, D3... Dn }

36 Our scheme of a bitemporal conceptual relation R Arbitrary number of explicit attribute from DA with domain in DD An implicit timestamp attribute T with domain DTT DVT Thus a tuple x in r(r), instance of R, x = ( a1, a2,... an tb )

37 10 VT 05 UC Sam, CSIE TT

38 ts_update(r, ct) { for each x r for each (UC, cv) x[ T ] x[ T ] = x[ T ] {(ct, cv)} } Performance Issue?

39 10 VT 05 Sam, CSIE TT

40 10 VT 05 Sam, CSIE TT

41 Bob, CSIE 10 VT 05 Sam, CSIE Sam, EE TT 15

42 Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05), (00, 95),..., (00, 10),..., (05, 95),..., (05, 10), (05, 00),...,(05, 05),... (10, 00),..., (10, 05)} Sam EE { (UC, 00),..., (UC, 05) } Bob CSIE { (UC, 10),..., (UC, 15) } VT Bob, CSIE Sam, CSIE Sam, EE TT

43 Insert, Delete & Modify

44 Delete Input r - relation in which tuple to be deleted (a1, a2,..., an) - qualified attributes of tuple to be deleted e.g. delete from r where a2 = 3

45 Delete (cont.) uc_ts(t b) = { (UC, cv) (UC, cv) tb } There s qualified tuples in relation r if t b s.t. (a1, a2,..., an tb) r Delete it (remove all chronons (UC, cv) ) r { (a1, a2,..., an tb) } { (a1, a2,..., an tb uc_ts(tb)) }

46 10 VT 05 Kan, CSIE Current TT 15

47 Insert Input r - relation to insert into (a1, a2,..., an) - attributes of tuple to insert tv - valid-time of tuple

48 Insert (cont.) New Record if t b s.t. (a1, a2,..., an tb) r Just Append r { (a 1, a2,..., an {UC} tv) }

49 Insert (cont.) Insert New Valid-Time to the tuple committed * before if t b s.t. (a1, a2,..., an tb) r AND ( (UC, c v) tb ) Insert New Portion of Valid-Time r { (a1, a2,..., an tb) } { (a1, a2,..., an tb { {UC} tv}) }

50 r { (a1, a2,..., an tb) } VT { (a1, a2,..., an tb { {UC} tv}) } Kan, CSIE Current TT 15

51 What if we want to insert new valid-time to current state?

52 10 VT 05 Kan, CSIE TT 15

53 Modify

54 modify(r, (a1, a2,..., an), tv) = insert ( delete (r, (a1, a2,..., an)), (a1, a2,..., an), tv )

55 10 VT 05 Kan, CSIE TT 15

56 Three Basic Operations

57 Delete delete (r, (a1, a2,..., an)) = r { (a1, a2,..., an tb) } { (a1, a2,..., an tb uc_ts(tb)) }, if tb s.t. (a1, a2,..., an tb) r r, otherwise

58 Insert insert (r, (a1, a2,..., an), tv) = r { (a 1, a2,..., an {UC} tv) }, if tb s.t. (a1, a2,..., an tb) r r { (a1, a2,..., an tb) } { (a1, a2,..., an tb { {UC} tv}) } r, otherwise, if tb s.t. (a1, a2,..., an tb) r ( (UC, cv) tb )

59 Modify modify (r, (a1, a2,..., an), tv) = insert ( delete (r, (a1, a2,..., an)), (a1, a2,..., an), tv), if tb s.t. (a1, a2,..., an tb) r ( (UC, cv) tb ) r, otherwise

60 Example

61 10 VT TT

62 10 VT 05 Sam, CSIE insert (Professor, ( Sam, CSIE ), [00, 05]) TT

63 10 VT 05 Sam, CSIE modify (Professor, ( Sam, CSIE ), [95, 10]) TT

64 10 VT 05 Sam, CSIE modify (Professor, ( Sam, CSIE ), [00, 05]) TT

65 Bob, CSIE 10 VT 05 Sam, CSIE Sam, EE delete (Professor, ( Sam, CSIE )) insert (Professor, ( Sam, EE ), [00, 05]) insert (Professor, ( Bob, CSIE ), [10, 15]) TT

66 What about select?

67 Transform Concept BCDM Represent

68 Transform BCDM Represent

69 Snodgrass Tuple Timestamped Representation Model [Sno 87]

70 R = (A1, A2,..., An, Ts, Te, Vs, Ve)

71 (Ts, Vs) (Te, Ve)

72 VT TT

73 Prof. Dept. Ts Te Vs Ve Sam CSIE Sam CSIE Sam CSIE Sam EE 10 UC Bob CSIE 10 UC VT Bob, CSIE Sam, CSIE Sam, EE TT

74 Transform BCDM Represent [Sno 87]

75 Transform BCDM [Sno 87]

76 Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05), (00, 95),..., (00, 10),..., (05, 95),..., (05, 10), (05, 00),...,(05, 05),... (10, 00),..., (10, 05)} Sam EE { (UC, 00),..., (UC, 05) } Bob CSIE { (UC, 10),..., (UC, 15) } Prof. Dept. Ts Te Vs Ve Sam CSIE Sam CSIE Sam CSIE Sam EE 10 UC Bob CSIE 10 UC 10 15

77 Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05), (00, 95),..., (00, 10),..., (05, 95),..., (05, 10), (05, 00),...,(05, 05),... (10, 00),..., (10, 05)} Prof. Dept. Ts Te Vs Ve Sam CSIE Sam CSIE Sam CSIE

78 Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05), (00, 95),..., (00, 10),..., (05, 95),..., (05, 10), (05, 00),...,(05, 05),... (10, 00),..., (10, 05)} Prof. Dept. Ts Te Vs Ve Sam CSIE Sam CSIE Sam CSIE

79 Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05), (00, 95),..., (00, 10),..., (05, 95),..., (05, 10), (05, 00),...,(05, 05),... (10, 00),..., (10, 05)} Covering function Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05) } Sam CSIE { (00, 95),..., (00, 10),..., (05, 95),..., (05, 10) } Sam CSIE { (05, 00),...,(05, 05),... (10, 00),..., (10, 05) }

80 Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05) } Sam CSIE { (00, 95),..., (00, 10),..., (05, 95),..., (05, 10) } Sam CSIE { (05, 00),...,(05, 05),... (10, 00),..., (10, 05) } Prof. Dept. Ts Te Vs Ve Sam CSIE Sam CSIE Sam CSIE

81 concept_to_snap(r ) { s = ; covering function for each x r z[ A ] = x[ A ]; for each t cover(x[ T ]) z[ Ts ] = min_ts(t) ; z[ Te ] = max_te(t) ; z[ Vs ] = min_vs(t) ; z[ Ve ] = max_ve(t) ; s = s { z } return s; }

82 Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05), (00, 95),..., (00, 10),..., (05, 95),..., (05, 10), (05, 00),...,(05, 05),... (10, 00),..., (10, 05)} Prof. Dept. Ts Te Vs Ve Sam CSIE Sam CSIE Sam CSIE

83 Prof. Dept. Ts Te Vs Ve Sam CSIE Sam CSIE Sam CSIE bi_chr function Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05) } Sam CSIE { (00, 95),..., (00, 10),..., (05, 95),..., (05, 10) } Sam CSIE { (05, 00),...,(05, 05),... (10, 00),..., (10, 05) }

84 Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05) } Sam CSIE { (00, 95),..., (00, 10),..., (05, 95),..., (05, 10) } Sam CSIE { (05, 00),...,(05, 05),... (10, 00),..., (10, 05) } Merge Prof. Dept T Sam CSIE { (95, 00),...,(95, 05),... (00, 00),..., (00, 05), (00, 95),..., (00, 10),..., (05, 95),..., (05, 10), (05, 00),...,(05, 05),... (10, 00),..., (10, 05)}

85 snap_to_concept(r) { s = ; for each z r r = r { z } x[ A ] = z [ A ]; x[ T ] = bi_chr( z[ T ], z[ V ]); for each y r if z[ A ] = y[ A ] r = r - { y }; x[ T ] = x[ T ] bi_chr( y[ T ], y[ V ]); s = s { x }; return s; }

86 Now, we have `insert`, `delete` and `modify` support from BCDM, and `select` operation propose by origins.

87 Performance Issue

88 Insert & Delete

89 [Sno87] BCDM Insert / Delete / Modify BCDM [Sno87]

90 insert(r, (a1, a2,..., an), tv) { cvr = coverv(tv); for each t cvr z[ A ] = (a1, a2,..., an); z[ Ts ] = ct; z[ Te ] = UC; z[ Vs ] = t[ s ]; z[ Ve ] = t[ e ]; r = r { z }; return r; }

91 delete(r, (a1, a2,..., an)) { for each x r if x[ A ] = (a1, a2,..., an) and x[ Te ] = UC x[ Te ] = ct; return r; }

92 Another 4 Representation Model Jensen s Backlog-Based Representation Scheme [Kim 78, JMR 93] R = (A1, A2,..., Vs, Ve, T, Op) Gadia s Attribute Value Timestamped Representation Scheme [Gad 88, Gad 92] R = ( {(Ts, Te) [Vs, Ve] A1},..., {(Ts, Te) [Vs, Ve] An} )

93 Another 4 Representation Model McKenzie s Attribute Value Timestamped Representation Scheme [Mck 88] [Ms 91] R = (T, (A1V1,..., AnVn)) Ben-Zvi s Tuple Timestamped Representation Scheme [BZ 82] R = (A1,..., An, Tes, Trs, Tee, Tre, Td)

94 snap_to_concept BCDM Transform concept_to_snap + Delete + Insert Represent

95 Want more?

96 What things make the RDBM so powerful

97 Relational Algebra π, σ,,,

98 Daunting Task? [Soo 91] [SS 88] [McKenzie 86] [BADW 82]

99 We want to focus on... Data Representation Data Storage Query Evaluation Compatible

100 Thanks!