aggregate sum retrieval in sensor network by distributed prefix sum data cube lok hang lee and man...
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Aggregate sum retrieval in sensor network by distributed prefix sum data
cube
Lok Hang Lee and Man Hon WongThe Chinese University of Hong Kong
Department of Computer Science and Engineering
19th International Conference on Advanced Information Networking and Applications (AINA’05)
OUTLINE
1. Introduction 2. Prefix Sum Data Cube 3. Building Distributed PS Data Cube 4. Simulation 5. Conclusion
1. Introduction
Data aggregate important data retrieval problems
Common operation like SUM, AVG, MAX, and MIN
Construct a distributed data cube
Distributed prefix sum data cube in autonomous way
Fast and simultaneous retrievals of aggregate sum data on any rectangular region
(a) A grid-like area and the readings of the cells(b) The PS data cube of that area
0 1 2 3
(a) (b)
2. Prefix Sum Data Cube
A 2-D grid every cell of the grid holds a numeric value v(x,y)
PS data cube storing pre-computed data aggregates
Definition 1
Each cell locating at column Xi and row Yi
keeps a value v ( Xi , Yi )
Prefix sum s ( Xi , Yi ) stored in cell is
Yi
n
Xi
mnmv
00),(
12 45
27 2112+27+45+21 =105 12 57
39 105
X
Y
0 1
0
1
0 1
0
1
Definition 2
A prefix sum data cube is a grid of cells
in which each cell maintains a prefix sum.
Definition 3
Sum of all the cell values in the region e : f
Sum( e : f )
e : f is the rectangular region with sensors e being the anchor
f being the endpoint
Definition 4
X
e
f
X
e
f
0 1 2 3
e
f
c
b
a
Sum( e : f )
=s(f)-s(b)-s(c)+s(a)
=648-141-136+12
=383
3. Building Distributed PS Data Cube
Lemma1 – s(Xc,Yc)=v(Xc,Yc)+s(Xc-1,Yc)+s(Xc,Yc-1)
-s(Xc-1,Yc-1)
For any cell c located at
(Xc,Yc)
Three variables u(i) , l(i) , d(i) received from the upper, left, and the upper l
eft neighbors
Computes own prefix sum(Xi,Yi)
At time t locate (X,Y) X+Y=t to do calculate its prefix sum and broadcast
Lemma 2
At time t = X+Y, the prefix sums of all the nodes at (X,Y ) will be ready
0 1 2 3 4
0 1 2 3 4
TIME= 0
TIME= 1
TIME= 2
TIME= 3
TIME= 4
TIME= 5
TIME= 6
TIME= 7
TIME= 8
A Distributed PS data cube is beingconstructed in a sensor network
Lemma 3
With length = h and width =k, constructed in h +k - 2 units of time
EX: 5 + 5 - 2 = 8
EX1 ：aggregate sum=s(a)-s(b)-s(c)+s(d)
d
ab
cd
EX2 ： sum=s(a)-s(b)+s(c)-s(d)-s(e)+s(f)-s(d) -s(g)+s(h)
作者算錯 ,多減
a
bcdh
g f
e
Querying the aggregate sums ofseveral regions simultaneously
4. Simulation
Construction time
Width : h
Length : K
h + k = 200
100+100-2=198
10
10
Network Traffic
Width : h
Length : K
5. Conclusion
Use a distributed prefix sum (PS) data cube to facilitate the retrieval of aggregate sums from multiple regions
In worst case, the algorithm only takes O(N) time
(a) Network traffic against different network sizes
60
50
40
30
20
10
0
Network traffic against different network sizes