1. dop d d 1 2
reconst
reconst
sop P P 1 2

2. a u c t i o n i t e m i t e m i d : 5 1 d e s c : b i d i d : 4 3 3 d e s c : 1 9 7 1 T r e k 5 9 M a r t i n S u p e r l i g h t G u i t a r b i d d e r : a m t : R o a d B i k e J o e $ 1 5

3. a u c t i o n i t e m i d : 5 1 b i d b i d d e r : a m t : S u e $ 1 5 5

4. a u c t i o n i t e m i t e m i d : 5 1 d e s c : b i d b i d i d : 4 3 3 d e s c : 1 9 7 1 T r e k 5 9 M a r t i n S u p e r l i g h t G u i t a r b i d d e r : a m t : b i d d e r : a m t : R o a d B i k e J o e $ 1 5 S u e $ 1 5 5

7. Differential Nest Old Value New Value Subject, Title
Subject, Title Subject, Title
Subject, Title
produce partial result
( null, null, Google, {Title1}),
( null, null, Microsoft, {Title2, Title3})
(Google, Title1),
(Microsoft, Title2),
(Microsoft, Title3)
(Google, {Title1}, Google, {Title1, Title4})
(Google, Title4)
(Google, {Title1,Title4}, Google, {Title1, Title4,
Title 5})
(Google, Title5)
but what you’d really like to send is: (Google, {Title5})
and “merge” it with: (Google, {Title1,Title4})
Subject: Google
Title: Title1
Title: Title4
Title: Title5
Title:Title4
Merge

8. Merge Example Combined Inserted Used in Match Merged Document
auction
item
item
iid:501
desc: Trek Madone 5.9 Bike
bid
bid
iid:433
desc: 1971 Martin Guitar
bidder: Dave
amt: $1500
bidder: Sue
amt: $1550
Merged Document
auction
auction
item
item
item
iid:501
desc: Trek Madone 5.9 Bike
bid
iid:433
desc: 1971 Martin Guitar
iid:501
bid
bidder: Dave
amt: $1500
bidder: Sue
amt: $1550
Auction Document
New Bid

9. Merge Template (MT)
(auction, [], NoContentNoAttrs)
auction
(item, [iid], NoContentNoAttrs)
item
(iid, [], ExactMatch)
(desc, [], ShallowContent - Replace)
iid:501
(bid, [bidder, amt], NoContentNoAttrs)
bid
(bidder, [], ExactMatch)
(amt, [], ExactMatch)
bidder: Sue
amt: $1550
Merge Template is an XML document consisting of a tree of Element Merge Templates (EMT)
EMT is a triplet containing: (name, local key, content combine function)

10. View Merge as Least Upper Bound
auction
item
item
iid:501
desc: Trek Madone 5.9 Bike
bid
bid
iid:433
desc: 1971 Martin Guitar
bidder: Dave
amt: $1500
bidder: Sue
amt: $1550
Merged Document (D3)
D3 is “smallest” document that “contains” D1 and D2
auction
auction
item
item
item
iid:501
desc: Trek Madone 5.9 Bike
bid
id:433
desc: 1971 Martin Guitar
iid:501
bid
bidder: Dave
amt: $1500
bidder: Sue
amt: $1550
Auction Document (D1)
New Bid (D2)

11. What can go wrong? No unique result (no Least Upper Bound (LUB))
Keys in Merge Template eliminate ambiguity
Know D4 is correct result if we know iid is a key for item
auction
auction
item
item
item
iid:501
iid:433
iid:501
iid:433 D3 D4
auction
auction
Id as key to eliminate D4
item
item
iid:501
iid:433 D1 D2

12. Non-Key-Respecting Documents
auction
auction
(auction, [], NoContentNoAttrs)
item
item
item
(item, [iid], NoContentNoAttrs)
iid:501
iid:433
iid:501
iid:433
(iid, [], ExactMatch) D3 D4 T
means contained in. D is contained in D′ if there is a structure-preserving mapping from D into D′
D3 is not key-respecting with respect to T and should not be in LT.
auction
auction
item
item
iid:501
iid:433 D1 D2

13. Merge-Lattice Theorem OverviewD3
ρ(D1)
ρ(D2) LT    D1 D2
ρ(D1)
ρ(D2) ρ1 ρ2
Associate each document D with a unique path set ρ(D)
ρ(D1)  ρ(D2) is a Least Upper Bound (LUB) for ρ(D1) and ρ(D2)
ρ(D1)  ρ(D2) is the “smallest” set that contains both ρ(D1) and ρ(D2)
Intuition: Merge of D1 and D2 should be the document associated with ρ(D1)  ρ(D2)

14. Document and Path Set Use Merge Template + document to create path set
auction[]:
auction[].item[id:501]:
auction[].item[id:501].id[]:501
auction[].item[id:501].desc[]:Trek Madone 5.9 Bike
auction[].item[id:501].bid[bidder:Dave,amt:$1500]:
auction[].item[id:501].bid[bidder:Dave,amt:$1500].
bidder[]:Dave
amt[]:$1500
auction
item
iid:501
desc:
Trek
Madone
5.9 Bike
bid
bidder:
Dave
amt: $1500
auction[].item[iid:501].desc[]:Trek Madone 5.9 Bike
rooted key value
element content
Use Merge Template + document to create path set
One element in path set for each element in document
Path comprised of rooted key value and element content
Path set order (subset) identical to document containment order

15. Proof that D3 is in L D3 3
σ σ-1 (=ρ3) T 2 ρ2
ρ(D1)
ρ(D2)  D2 1
ρ2-1 ρ1 D1
ρ1-1
Construct D3 from ρ(D1)  ρ(D2), show D3 is compatible and key-respecting with respect to T

17. Figure 2: Using Panes to Evaluate Query 1
(item-id, bid-price, timestamp)
(10, $9.12, 12:15:52 PM) t1
(11, $8.93, 12:16:42 PM) t2
(11, $9.20, 12:16:49 PM) t3
(pane-max, pane-timestamp)
($9.12, 12:15:52 PM) p1
($9.20, 12:16:49 PM) p2
(win-max, timestamp)
($9.12, 12:15:52 PM) w1
($9.20, 12:16:49 PM) w2
streamscan
window-max (bid-price)
RANGE = 1 min
SLIDE = 1 min
WATTR = timestamp
RANGE = 4 min
WATTR = pane-timestamp
Figure 2: Using Panes to Evaluate Query 1

19. Figure 5: Cost Ratio of Pane vs. Original Window-Id Approach

20. Figure 6: Band Disorder

21. Figure 7: Block-sorted Disorder

22. Figure 8: Latency vs. Accuracy Band-Disorder
(average error percentage)

23. Figure 9: Latency vs. Accuracy Block-Sorted-Disorder
(average error percentage)

24. Figure 10: Latency vs. Accuracy Block-Sorted- Disorder
(percentage of wrong answers)

25. Figure 1: Four detection stations in a detection task
SUSPECT
PRESUMPTIVE
CONFIRMED
INTERCEPTED
Figure 1: Four detection stations in a detection task
(from Yonnel Gardes, The Transpo Group, Kirkland, WA, with permission)

26. Figure 4: Example of insertion, initialization, and update of bins as new tuples arrive.

28. Figure 8 (b): Execution Time: WID versus Buffering – Zoom-in

29. Figure 10: Latency vs. Accuracy Block-Sorted- Disorder (percentage of incorrect answer)
external punctuation

30. count(*) count (*) bucket streamscan (group on window-id,
(sensor-id, room-id, timestamp,
temperature)
(2, C, 00:05:58PM, 80°) T0
(2, C, 00:06:05PM, 82°) T1
(item-id, bid-price, auction-site,
timestamp, pane-id)
(3, 5, 00:05:58PM, 80°, 5-5) T0
(*, C, * , * , 5) P1
(2, C, 00:06:05 PM, 83°, 6-6) T1
streamscan
count (*)
(group on pane-id,
auction-site)
bucket
RANGE = 1 min
SLIDE = 1 min
WINATTR = timestamp
RANGE = 5
SLIDE = 1
WINATTR = pane-id
count(*)
(group on window-id,
(auction-site, pane-id, count,
timestamp)
(3, 5, 8, 00:05:42PM) M0
timestamp, window-id)
(3, 5, 8, 00:05:42PM, 6-10) M0