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Efficient data collec-on in par-cipatory sensing
Runwei Zhang,
joint work with Zichong Chen,LCAV,EPFL
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Contents
‣ Introduc<on
‣ Our 2-‐step adap<ve algorithm
‣ Simula<on results
‣ Problem formula<on
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
‣Sensors equipped
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
‣Sensors equipped
Cameras
GPS
Microphones
Compass
Gyroscope
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
Thermometer
Hygrometer
Barometer
CO,CO2,NO,O3
‣Sensors equipped
Cameras
GPS
Microphones
Compass
Gyroscope
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
Thermometer
Hygrometer
Barometer
CO,CO2,NO,O3
‣ How it works‣Sensors equipped
Cameras
GPS
Microphones
Compass
Gyroscope
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
Thermometer
Hygrometer
Barometer
CO,CO2,NO,O3
‣ How it works‣Sensors equipped
Cameras
GPS
Microphones
Compass
Gyroscope
Mobile sensor
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
‣ Achieve certain overall objec<ve‣ Reconstruct noise/temperature map
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
‣ Cost per sensor reading‣ Energy consump<on
‣ Network bandwidth‣ Privacy leakage
‣ Achieve certain overall objec<ve‣ Reconstruct noise/temperature map
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Background in par-cipatory sensing
‣ Cost per sensor reading‣ Energy consump<on
‣ Network bandwidth‣ Privacy leakage
‣ Achieve certain overall objec<ve‣ Reconstruct noise/temperature map
Reduce unnecessary sensor readings?
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Why can we turn off some sensors?
Sensor Coverage range
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Why can we turn off some sensors?
All sensors always ac<ve
Sensor Coverage range
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Why can we turn off some sensors?
All sensors always ac<ve
Sensor Coverage range
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Why can we turn off some sensors?
All sensors always ac<ve
Sensor Coverage range
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Why can we turn off some sensors?
All sensors always ac<ve ANer turning off
Sensor Coverage range
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Why can we turn off some sensors?
All sensors always ac<ve ANer turning off
Sensor Coverage range
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Objec-ve & Challenge
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Objec-ve & Challenge
‣ Objec<ve
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Objec-ve & Challenge
‣ Objec<ve‣ Exploit the spa6al correla6ons
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Objec-ve & Challenge
‣ Objec<ve‣ Exploit the spa6al correla6ons‣ Reduce data readings
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Objec-ve & Challenge
‣ Objec<ve‣ Exploit the spa6al correla6ons‣ Reduce data readings‣ Maintain coverage (small reconstruc6on error)
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Objec-ve & Challenge
‣ Objec<ve‣ Exploit the spa6al correla6ons‣ Reduce data readings‣ Maintain coverage (small reconstruc6on error)
‣ Achieve fairness
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Objec-ve & Challenge
‣ Objec<ve‣ Exploit the spa6al correla6ons‣ Reduce data readings‣ Maintain coverage (small reconstruc6on error)
‣ Achieve fairness
‣ Challenge
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Objec-ve & Challenge
‣ Objec<ve‣ Exploit the spa6al correla6ons‣ Reduce data readings‣ Maintain coverage (small reconstruc6on error)
‣ Achieve fairness
‣ Challenge‣ Sensors’ moving trajectories unknown
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Objec-ve & Challenge
‣ Objec<ve‣ Exploit the spa6al correla6ons‣ Reduce data readings‣ Maintain coverage (small reconstruc6on error)
‣ Achieve fairness
‣ Challenge‣ Sensors’ moving trajectories unknown‣ Decisions should be made online
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Contents
‣ Introduc<on
‣ Our 2-‐step adap<ve algorithm
‣ Simula<on results
‣ Problem formula<on
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
‣ Maximum coverage problem
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
‣ Maximum coverage problem
Sensor Coverage range
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
‣ Maximum coverage problem
Sensor Coverage range
Reduce
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
‣ Maximum coverage problem
Sensor Coverage range
Objec<ve: Maximize number of covered cells
Constraint: Number of ac<ve sensor
Reduce
Friday, May 24, 13
s6
s7
y7
y8
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
s1
s2
s3
s4
s5
y1y2
y3
y4
y5
y6
Sensors Cells
Friday, May 24, 13
s6
s7
y7
y8
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
s1
s2
s3
s4
s5
y1y2
y3
y4
y5
y6
Sensors Cells
A B: A can sense B
Friday, May 24, 13
Max
X
ej2E
yj
s.t.
X
i
si k
X
ej2Ai
si � yj
0 yi 1, si 2 {0, 1}.s6
s7
y7
y8
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
s1
s2
s3
s4
s5
y1y2
y3
y4
y5
y6
Sensors Cells
A B: A can sense B
Friday, May 24, 13
Max
X
ej2E
yj
s.t.
X
i
si k
X
ej2Ai
si � yj
0 yi 1, si 2 {0, 1}.s6
s7
y7
y8
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
s1
s2
s3
s4
s5
y1y2
y3
y4
y5
y6
Sensors Cells
A B: A can sense B
k=5?
Friday, May 24, 13
Max
X
ej2E
yj
s.t.
X
i
si k
X
ej2Ai
si � yj
0 yi 1, si 2 {0, 1}.s6
s7
y7
y8
LCAV – AudioVisual Communica1ons Laboratory
The sta-c sensor networks
s1
s2
s3
s4
s5
y1y2
y3
y4
y5
y6
Sensors Cells
A B: A can sense B
k=5?
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenarioAt 6me slot n=1:
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
12
3
45
6
At 6me slot n=1:
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
12
3
45
6
At 6me slot n=1:
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
12
3
45
6
At 6me slot n=1:
Reduce
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
12
3
45
6
At 6me slot n=1:
Reduce
12
3
45
6
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
12
3
45
6
At 6me slot n=1:
At 6me slot n=2:
Reduce
12
3
45
6
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
12
3
45
6
At 6me slot n=1:
1
2
3
4 56
At 6me slot n=2:
Reduce
12
3
45
6
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
12
3
45
6
At 6me slot n=1:
1
2
3
4 56
At 6me slot n=2:
Reduce
12
3
45
6
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
12
3
45
6
At 6me slot n=1:
1
2
3
4 56
At 6me slot n=2:
Reduce
Reduce
12
3
45
6
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
12
3
45
6
At 6me slot n=1:
1
2
3
4 56
At 6me slot n=2:
Reduce
Reduce
12
3
45
6
1
2
3
4 56
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
At 6me slot n=1
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
Sensor
12
3
45
6
At 6me slot n=1
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
Sensor
12
3
45
6
At 6me slot n=1
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
Sensor
12
3
45
6
At 6me slot n=1
b(n) = A(n) · s(n)
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...
A B: A resides in B
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
Sensor
12
3
45
6
At 6me slot n=1 y(n)1
y(n)2
y(n)3
y(n)4
y(n)5
y(n)6
y(n)7
Cells...
...
B C: B can sense C
b(n) = A(n) · s(n)
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...
A B: A resides in B
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
Sensor
12
3
45
6
At 6me slot n=1 y(n)1
y(n)2
y(n)3
y(n)4
y(n)5
y(n)6
y(n)7
Cells...
...
B C: B can sense C
b(n) = A(n) · s(n)
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...
A B: A resides in B
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
At 6me slot n=2
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
Sensor
1
2
3
4 56
At 6me slot n=2
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
Sensor
1
2
3
4 56
At 6me slot n=2s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
s(n)2
Sensors
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
Sensor
1
2
3
4 56
At 6me slot n=2s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
s(n)2
Sensors
...
A B: A resides in B
...b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
b(n) = A(n) · s(n)
Sensor loca6ons
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
Sensor
1
2
3
4 56
At 6me slot n=2s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
s(n)2
Sensors
...
B C: B can sense C
...y(n)1
y(n)2
y(n)3
y(n)4
y(n)5
y(n)6
y(n)7
Cells
...
A B: A resides in B
...b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
b(n) = A(n) · s(n)
Sensor loca6ons
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
The par-cipatory sensing scenario
Sensor
1
2
3
4 56
At 6me slot n=2s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
s(n)2
Sensors
...
B C: B can sense C
...y(n)1
y(n)2
y(n)3
y(n)4
y(n)5
y(n)6
y(n)7
Cells
...
A B: A resides in B
...b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
b(n) = A(n) · s(n)
Sensor loca6ons
Friday, May 24, 13
Max
0
@lim inf
n!1
1
n
nX
t=1
X
ej2E
y(n)j ,� lim sup
n!1V (✓(n)
)
1
A
s.t. eT · s(n) k, 8n 2 N+
A(n) · s(n) = b(n), 8n 2 N+
X
ej2Ai
s(n)i � y(n)j , 8n 2 N+
✓(n)=
1
n
nX
t=1
s(t), 8n 2 N+
0 y(n)i 1, s(n)i 2 {0, 1}, 8n 2 N+.
LCAV – AudioVisual Communica1ons Laboratory
Op-mal schedule with known trajectories
13
Friday, May 24, 13
Max
0
@lim inf
n!1
1
n
nX
t=1
X
ej2E
y(n)j ,� lim sup
n!1V (✓(n)
)
1
A
s.t. eT · s(n) k, 8n 2 N+
A(n) · s(n) = b(n), 8n 2 N+
X
ej2Ai
s(n)i � y(n)j , 8n 2 N+
✓(n)=
1
n
nX
t=1
s(t), 8n 2 N+
0 y(n)i 1, s(n)i 2 {0, 1}, 8n 2 N+.
LCAV – AudioVisual Communica1ons Laboratory
Op-mal schedule with known trajectories
13
coverage
Friday, May 24, 13
Max
0
@lim inf
n!1
1
n
nX
t=1
X
ej2E
y(n)j ,� lim sup
n!1V (✓(n)
)
1
A
s.t. eT · s(n) k, 8n 2 N+
A(n) · s(n) = b(n), 8n 2 N+
X
ej2Ai
s(n)i � y(n)j , 8n 2 N+
✓(n)=
1
n
nX
t=1
s(t), 8n 2 N+
0 y(n)i 1, s(n)i 2 {0, 1}, 8n 2 N+.
LCAV – AudioVisual Communica1ons Laboratory
Op-mal schedule with known trajectories
13
coverage fairness
Friday, May 24, 13
Max
0
@lim inf
n!1
1
n
nX
t=1
X
ej2E
y(n)j ,� lim sup
n!1V (✓(n)
)
1
A
s.t. eT · s(n) k, 8n 2 N+
A(n) · s(n) = b(n), 8n 2 N+
X
ej2Ai
s(n)i � y(n)j , 8n 2 N+
✓(n)=
1
n
nX
t=1
s(t), 8n 2 N+
0 y(n)i 1, s(n)i 2 {0, 1}, 8n 2 N+.
LCAV – AudioVisual Communica1ons Laboratory
Op-mal schedule with known trajectories
13
coverage fairness
Number of ac6ve sensors
Friday, May 24, 13
Max
0
@lim inf
n!1
1
n
nX
t=1
X
ej2E
y(n)j ,� lim sup
n!1V (✓(n)
)
1
A
s.t. eT · s(n) k, 8n 2 N+
A(n) · s(n) = b(n), 8n 2 N+
X
ej2Ai
s(n)i � y(n)j , 8n 2 N+
✓(n)=
1
n
nX
t=1
s(t), 8n 2 N+
0 y(n)i 1, s(n)i 2 {0, 1}, 8n 2 N+.
LCAV – AudioVisual Communica1ons Laboratory
Op-mal schedule with known trajectories
13
coverage fairness
Number of ac6ve sensors
Adap6ve algorithms?
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Contents
‣ Introduc<on
‣ Our 2-‐step adap<ve algorithm
‣ Simula<on results
‣ Problem formula<on
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Step 1: choose subsets of cells
Friday, May 24, 13
Sensor
12
3
45
6
LCAV – AudioVisual Communica1ons Laboratory
Step 1: choose subsets of cells
Friday, May 24, 13
Sensor
12
3
45
6
LCAV – AudioVisual Communica1ons Laboratory
Step 1: choose subsets of cells
Friday, May 24, 13
Sensor
12
3
45
6
LCAV – AudioVisual Communica1ons Laboratory
Step 1: choose subsets of cells
y(n)1
y(n)2
y(n)3
y(n)4
y(n)5
y(n)6
y(n)7
Cells...
...
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...
Friday, May 24, 13
Sensor
12
3
45
6
Max lim inf
n!1
1
n
nX
t=1
X
ej2E
y(n)j
s.t. eT · b(n) k, 8n 2 N+
X
ej2Ai
b(n)i � y(n)j , 8n 2 N+
A(n) · e � b(n), 8n 2 N+
0 y(n)i 1, 8n 2 N+
b(n)i 2 {0, 1}, 8n 2 N+.
LCAV – AudioVisual Communica1ons Laboratory
Step 1: choose subsets of cells
y(n)1
y(n)2
y(n)3
y(n)4
y(n)5
y(n)6
y(n)7
Cells...
...
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...
Friday, May 24, 13
Sensor
12
3
45
6
Max lim inf
n!1
1
n
nX
t=1
X
ej2E
y(n)j
s.t. eT · b(n) k, 8n 2 N+
X
ej2Ai
b(n)i � y(n)j , 8n 2 N+
A(n) · e � b(n), 8n 2 N+
0 y(n)i 1, 8n 2 N+
b(n)i 2 {0, 1}, 8n 2 N+.
LCAV – AudioVisual Communica1ons Laboratory
Step 1: choose subsets of cells
y(n)1
y(n)2
y(n)3
y(n)4
y(n)5
y(n)6
y(n)7
Cells...
...
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...{A(n)}n2N+{b(n)}n2N+ is decided by
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Step 2: choose ac-ve sensors within cells
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Step 2: choose ac-ve sensors within cells
Sensor
12
3
45
6
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Step 2: choose ac-ve sensors within cells
Sensor
12
3
45
6
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...A(n)
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Step 2: choose ac-ve sensors within cells
Sensor
12
3
45
6
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...A(n)
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Step 2: choose ac-ve sensors within cells
Sensor
12
3
45
6
Min lim supn!1
V (✓(n))
s.t. A(n) · s(n) = b(n), 8n 2 N+
✓(n) =1
n
nX
t=1
s(t), 8n 2 N+
s(n) 2 {0, 1}M , 8n 2 N+.
ORIGINAL-‐OPT:s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...A(n)
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Step 2: choose ac-ve sensors within cells
Sensor
12
3
45
6
Min lim supn!1
V (✓(n))
s.t. A(n) · s(n) = b(n), 8n 2 N+
✓(n) =1
n
nX
t=1
s(t), 8n 2 N+
s(n) 2 {0, 1}M , 8n 2 N+.
ORIGINAL-‐OPT:s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...A(n)
Adap6ve algorithms?
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
“Let the laziest serve” (LLS)
At 6me slot n
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
“Let the laziest serve” (LLS)
✓(n�1)m =
1
n� 1
n�1X
t=1
s(t)m , 8m
(1) Calculate the frac6on of ac6ve sensing 6mes for each sensor
At 6me slot n
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
“Let the laziest serve” (LLS)
✓(n�1)m =
1
n� 1
n�1X
t=1
s(t)m , 8m
(1) Calculate the frac6on of ac6ve sensing 6mes for each sensor
(2) Within each chosen cell,choose the ac6ve sensor
with the smallest
m
✓(n�1)m
At 6me slot n
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
“Let the laziest serve” (LLS)
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...
✓(n�1)m =
1
n� 1
n�1X
t=1
s(t)m , 8m
(1) Calculate the frac6on of ac6ve sensing 6mes for each sensor
(2) Within each chosen cell,choose the ac6ve sensor
with the smallest
m
✓(n�1)m
At 6me slot n
Friday, May 24, 13
✓(n�1)3 < ✓(n�1)
2
LCAV – AudioVisual Communica1ons Laboratory
“Let the laziest serve” (LLS)
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...
✓(n�1)m =
1
n� 1
n�1X
t=1
s(t)m , 8m
(1) Calculate the frac6on of ac6ve sensing 6mes for each sensor
(2) Within each chosen cell,choose the ac6ve sensor
with the smallest
m
✓(n�1)m
At 6me slot n
Friday, May 24, 13
✓(n�1)3 < ✓(n�1)
2
✓(n�1)6 < ✓(n�1)
5
LCAV – AudioVisual Communica1ons Laboratory
“Let the laziest serve” (LLS)
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...
✓(n�1)m =
1
n� 1
n�1X
t=1
s(t)m , 8m
(1) Calculate the frac6on of ac6ve sensing 6mes for each sensor
(2) Within each chosen cell,choose the ac6ve sensor
with the smallest
m
✓(n�1)m
At 6me slot n
Friday, May 24, 13
✓(n�1)3 < ✓(n�1)
2
✓(n�1)6 < ✓(n�1)
5
LCAV – AudioVisual Communica1ons Laboratory
“Let the laziest serve” (LLS)
s(n)1
s(n)3
s(n)4
s(n)5
s(n)6
Sensors
s(n)2
b(n)1
b(n)2
b(n)3
b(n)4
b(n)5
b(n)6
b(n)7
Sensor loca6ons...
...
✓(n�1)m =
1
n� 1
n�1X
t=1
s(t)m , 8m
(1) Calculate the frac6on of ac6ve sensing 6mes for each sensor
(2) Within each chosen cell,choose the ac6ve sensor
with the smallest
m
✓(n�1)m
At 6me slot n
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Gradient upda-ng direc-on
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Gradient upda-ng direc-on
@V (✓)
@✓i>
@V (✓)
@✓j✓i > ✓j
When the objec6ve func6on fulfills
if
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Gradient upda-ng direc-on
@V (✓)
@✓i>
@V (✓)
@✓j✓i > ✓j
When the objec6ve func6on fulfills
if nega6ve entropy Lp-‐norm
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Gradient upda-ng direc-on
@V (✓)
@✓i>
@V (✓)
@✓j✓i > ✓j
When the objec6ve func6on fulfills
if
s(n)LLS let be op6mal w.r.t the linearized problem
nega6ve entropy Lp-‐norm
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Gradient upda-ng direc-on
@V (✓)
@✓i>
@V (✓)
@✓j✓i > ✓j
When the objec6ve func6on fulfills
if
s(n)LLS let be op6mal w.r.t the linearized problem
nega6ve entropy Lp-‐norm
Min r>V (✓(n�1)) · xs.t. A
(n) · x = b
(n),
x 2 [0, 1]M .
ORIGINAL-‐LINEARIZED:
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Gradient upda-ng direc-on
@V (✓)
@✓i>
@V (✓)
@✓j✓i > ✓j
When the objec6ve func6on fulfills
if
s(n)LLS let be op6mal w.r.t the linearized problem
nega6ve entropy Lp-‐norm
Min r>V (✓(n�1)) · xs.t. A
(n) · x = b
(n),
x 2 [0, 1]M .
ORIGINAL-‐LINEARIZED:
integer constraints are changed into non-‐integer ones
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chainsSensor 1
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chainsSensor 1 Sensor 2
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chainsSensor 1 Sensor 2
...
...
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chainsSensor 1 Sensor 2
A(n) 2 {A[1],A[2],A[3] · · · }
Trajectories of all sensorsare drawn from a large markov chain
...
...
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chainsSensor 1 Sensor 2
A(n) 2 {A[1],A[2],A[3] · · · }
Trajectories of all sensorsare drawn from a large markov chain
Min V (⇥)
s.t. A[l] · q[l] = b[l], l = 1, · · ·L,
⇥ =LX
l=1
Pl · q[l], l = 1, · · ·L
q[l] 2 {0, 1}M , l = 1, · · ·L.
MARKOV-‐OPT:
...
...
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chainsSensor 1 Sensor 2
A(n) 2 {A[1],A[2],A[3] · · · }
Trajectories of all sensorsare drawn from a large markov chain
Min V (⇥)
s.t. A[l] · q[l] = b[l], l = 1, · · ·L,
⇥ =LX
l=1
Pl · q[l], l = 1, · · ·L
q[l] 2 {0, 1}M , l = 1, · · ·L.
MARKOV-‐OPT:
...
...
Pl is the sta6onary distribu6on A(n) = A[l]
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
Friday, May 24, 13
A(n) : A[3],A[1],A[2],A[4],A[2],A[3],A[1],A[4],A[3], · · ·
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
Friday, May 24, 13
A(n) : A[3],A[1],A[2],A[4],A[2],A[3],A[1],A[4],A[3], · · ·
n : 1, 2, 3, 4, 5, 6, 7, 8,
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
Friday, May 24, 13
A(n) : A[3],A[1],A[2],A[4],A[2],A[3],A[1],A[4],A[3], · · ·
n : 1, 2, 3, 4, 5, 6, 7, 8,
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
Friday, May 24, 13
A(n) : A[3],A[1],A[2],A[4],A[2],A[3],A[1],A[4],A[3], · · ·
n : 1, 2, 3, 4, 5, 6, 7, 8,
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
Friday, May 24, 13
A(n) : A[3],A[1],A[2],A[4],A[2],A[3],A[1],A[4],A[3], · · ·
n : 1, 2, 3, 4, 5, 6, 7, 8,
n1 n2 n3
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
Friday, May 24, 13
A(n) : A[3],A[1],A[2],A[4],A[2],A[3],A[1],A[4],A[3], · · ·
n : 1, 2, 3, 4, 5, 6, 7, 8,
n1 n2 n3
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
Ev(j)l =Pl
P3, The expected 6mes that
during the recurrent round obeys sta6onaryj
A(n) = A[l]
Friday, May 24, 13
A(n) : A[3],A[1],A[2],A[4],A[2],A[3],A[1],A[4],A[3], · · ·
n : 1, 2, 3, 4, 5, 6, 7, 8,
n1 n2 n3
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
n 2 [nj�1 + 1, nj ] A(n) = A[l]At each 6me with , is op6mal w.r.ts(n)
Ev(j)l =Pl
P3, The expected 6mes that
during the recurrent round obeys sta6onaryj
A(n) = A[l]
Friday, May 24, 13
A(n) : A[3],A[1],A[2],A[4],A[2],A[3],A[1],A[4],A[3], · · ·
n : 1, 2, 3, 4, 5, 6, 7, 8,
n1 n2 n3
Min r>V (✓(n�1)) · xs.t. A
[l] · x(n) = b
[l],
x 2 [0, 1]M .
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
n 2 [nj�1 + 1, nj ] A(n) = A[l]At each 6me with , is op6mal w.r.ts(n)
Ev(j)l =Pl
P3, The expected 6mes that
during the recurrent round obeys sta6onaryj
A(n) = A[l]
Friday, May 24, 13
A(n) : A[3],A[1],A[2],A[4],A[2],A[3],A[1],A[4],A[3], · · ·
n : 1, 2, 3, 4, 5, 6, 7, 8,
n1 n2 n3
Min r>V (✓(n�1)) · xs.t. A
[l] · x(n) = b
[l],
x 2 [0, 1]M .
⇡Min r>V (✓(nj�1)) · xs.t. A
[l] · x(n) = b
[l],
x 2 [0, 1]M .
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
n 2 [nj�1 + 1, nj ] A(n) = A[l]At each 6me with , is op6mal w.r.ts(n)
Ev(j)l =Pl
P3, The expected 6mes that
during the recurrent round obeys sta6onaryj
A(n) = A[l]
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
During each recurrent round , n 2 [nj�1 + 1, nj ]
Friday, May 24, 13
P1/P3Ev(j)l
Min r>V (✓(nj�1)) · xs.t. A
[1] · x = b
[1],
x 2 [0, 1]M .
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
During each recurrent round , n 2 [nj�1 + 1, nj ]
Friday, May 24, 13
P1/P3Ev(j)l
Min r>V (✓(nj�1)) · xs.t. A
[1] · x = b
[1],
x 2 [0, 1]M .
P2/P3
Min r>V (✓(nj�1)) · xs.t. A
[2] · x = b
[2],
x 2 [0, 1]M .
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
During each recurrent round , n 2 [nj�1 + 1, nj ]
Friday, May 24, 13
P1/P3Ev(j)l
Min r>V (✓(nj�1)) · xs.t. A
[1] · x = b
[1],
x 2 [0, 1]M .
P2/P3
Min r>V (✓(nj�1)) · xs.t. A
[2] · x = b
[2],
x 2 [0, 1]M .
P3/P3
Min r>V (✓(nj�1)) · xs.t. A
[3] · x = b
[3],
x 2 [0, 1]M .
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
During each recurrent round , n 2 [nj�1 + 1, nj ]
Friday, May 24, 13
P1/P3Ev(j)l
Min r>V (✓(nj�1)) · xs.t. A
[1] · x = b
[1],
x 2 [0, 1]M .
P2/P3
Min r>V (✓(nj�1)) · xs.t. A
[2] · x = b
[2],
x 2 [0, 1]M .
P3/P3
Min r>V (✓(nj�1)) · xs.t. A
[3] · x = b
[3],
x 2 [0, 1]M .
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
...
...
During each recurrent round , n 2 [nj�1 + 1, nj ]
Friday, May 24, 13
P1/P3Ev(j)l
Min r>V (✓(nj�1)) · xs.t. A
[1] · x = b
[1],
x 2 [0, 1]M .
P2/P3
Min r>V (✓(nj�1)) · xs.t. A
[2] · x = b
[2],
x 2 [0, 1]M .
P3/P3
Min r>V (✓(nj�1)) · xs.t. A
[3] · x = b
[3],
x 2 [0, 1]M .
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
...
...
In all, is op6mal w.r.t the linearized version of MARKOV-‐OPT
During each recurrent round , n 2 [nj�1 + 1, nj ]
Friday, May 24, 13
P1/P3Ev(j)l
Min r>V (✓(nj�1)) · xs.t. A
[1] · x = b
[1],
x 2 [0, 1]M .
P2/P3
Min r>V (✓(nj�1)) · xs.t. A
[2] · x = b
[2],
x 2 [0, 1]M .
P3/P3
Min r>V (✓(nj�1)) · xs.t. A
[3] · x = b
[3],
x 2 [0, 1]M .
Min rTV (✓(nj�1)) ·LX
l=1
Plq[l]
s.t. A[l] · q[l] = b[l], l = 1, · · ·L,q[l] 2 {0, 1}M , l = 1, · · ·L.
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
...
...
In all, is op6mal w.r.t the linearized version of MARKOV-‐OPT
During each recurrent round , n 2 [nj�1 + 1, nj ]
Friday, May 24, 13
P1/P3Ev(j)l
Min r>V (✓(nj�1)) · xs.t. A
[1] · x = b
[1],
x 2 [0, 1]M .
P2/P3
Min r>V (✓(nj�1)) · xs.t. A
[2] · x = b
[2],
x 2 [0, 1]M .
P3/P3
Min r>V (✓(nj�1)) · xs.t. A
[3] · x = b
[3],
x 2 [0, 1]M .
Min rTV (✓(nj�1)) ·LX
l=1
Plq[l]
s.t. A[l] · q[l] = b[l], l = 1, · · ·L,q[l] 2 {0, 1}M , l = 1, · · ·L.
LCAV – AudioVisual Communica1ons Laboratory
When trajectories are from markov chains
LLS is asympto6cally op6mal
...
...
In all, is op6mal w.r.t the linearized version of MARKOV-‐OPT
During each recurrent round , n 2 [nj�1 + 1, nj ]
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Summary of the 2-‐step adap-ve algorithm
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Summary of the 2-‐step adap-ve algorithm
‣ Totally memoryless and adap<ve
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Summary of the 2-‐step adap-ve algorithm
‣ Totally memoryless and adap<ve
‣ Does not know trajectories in advance
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Summary of the 2-‐step adap-ve algorithm
‣ Totally memoryless and adap<ve
‣ Does not know trajectories in advance
‣ Achieves op<mal coverage in step 1
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Summary of the 2-‐step adap-ve algorithm
‣ Totally memoryless and adap<ve
‣ Does not know trajectories in advance
‣ Achieves op<mal coverage in step 1
‣ Achieves asympto<cally op<mal fairness in step 2
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Summary of the 2-‐step adap-ve algorithm
‣ Totally memoryless and adap<ve
‣ Does not know trajectories in advance
‣ Achieves op<mal coverage in step 1
‣ Achieves asympto<cally op<mal fairness in step 2
‣ Not necessarily op<mal when consider step 1 and step 2 jointly.
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Contents
‣ Introduc<on
‣ Our 2-‐step adap<ve algorithm
‣ Simula<on results
‣ Problem formula<on
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Simula-ons
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Simula-ons
‣ Bus trajectories‣ Synthesized from Lausanne bus <metables
‣ 327 buses, 400 bus stops, 18km*6km
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Simula-ons
‣ Bus trajectories‣ Synthesized from Lausanne bus <metables
‣ 327 buses, 400 bus stops, 18km*6km‣ Taxis trajectories‣ Real data from San Francisco
‣ 500 taxis, 30 days
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Simula-ons
‣ Bus trajectories‣ Synthesized from Lausanne bus <metables
‣ 327 buses, 400 bus stops, 18km*6km‣ Taxis trajectories‣ Real data from San Francisco
‣ 500 taxis, 30 days‣ We have not applied the reduc<on in step 1.
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Synthesizing Lausanne bus trajectories
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Synthesizing Lausanne bus trajectories
1 km
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Synthesizing Lausanne bus trajectories
1 km
‣ Acquire all the GPS loca<ons of 400 bus stops
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Synthesizing Lausanne bus trajectories
1 km
‣ Interpolate with <metables of 37 bus lines
‣ Acquire all the GPS loca<ons of 400 bus stops
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Synthesizing Lausanne bus trajectories
1 km
‣ Interpolate with <metables of 37 bus lines
‣ Acquire all the GPS loca<ons of 400 bus stops
‣ Add GPS noise, Poisson delay noise
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Energy efficiency
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Energy efficiency
‣ The obtained sensing schedule
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Energy efficiency
time / 10 minutes
bus
ID
100 200 300 400 500 600 700
50
100
150
200
250
300
‣ The obtained sensing schedule
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Energy efficiency
time / 10 minutes
bus
ID
100 200 300 400 500 600 700
50
100
150
200
250
300
Buses traveling to remote areas
‣ The obtained sensing schedule
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Energy efficiency
time / 10 minutes
bus
ID
100 200 300 400 500 600 700
50
100
150
200
250
300
Buses traveling to remote areas
Weekends
‣ The obtained sensing schedule
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Energy efficiency
time / 10 minutes
bus
ID
100 200 300 400 500 600 700
50
100
150
200
250
300
Buses traveling to remote areas
Weekends
‣ The obtained sensing schedule
‣ Energy savings
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Energy efficiency
time / 10 minutes
bus
ID
100 200 300 400 500 600 700
50
100
150
200
250
300
0.5 1 1.5 2 2.5 30
10
20
30
40
AI side length/km
Ener
gy sa
ving
s
Buses traveling to remote areas
Weekends
‣ The obtained sensing schedule
‣ Energy savings
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Energy efficiency
time / 10 minutes
bus
ID
100 200 300 400 500 600 700
50
100
150
200
250
300
0.5 1 1.5 2 2.5 30
10
20
30
40
AI side length/km
Ener
gy sa
ving
s
Buses traveling to remote areas
Weekends
‣ The obtained sensing schedule
‣ Energy savings
Friday, May 24, 13
−50 0 50 100 150 200 250 300 3500
0.05
0.1
0.15
0.2
Node idThe
ener
gy c
ost t
o th
e ba
selin
e
RandomOur algorithmOptimal
LCAV – AudioVisual Communica1ons Laboratory
Fairness
Sorted bus id
Active time ratio
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Using San Francisco taxis data
‣ Ac<ve sensing loca<ons accumulated with <me
Without our scheme With our scheme
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Energy efficiency & fairness
Friday, May 24, 13
LCAV – AudioVisual Communica1ons Laboratory
Future works
‣ Validate the reconstruc<on error‣ Consider temporal correla<ons
x
y
t
Friday, May 24, 13
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