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![Page 1: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/1.jpg)
Haiming Jin, He Huang, Lu Su and Klara Nahrstedt
University of Illinois at Urbana-ChampaignState University of New York at Buffalo
October 22, 2014
Cost-minimizing Mobile Access Point Deployment in Workflow-based Mobile
Sensor Networks
![Page 2: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/2.jpg)
Motivation
2Presenter: Haiming Jin
• Emerging mission-driven workflow-based mobile sensor networks• Airplane maintenance
• Mobile devices collect data• Workflow gives mobility information
image or video
text note
1:00 PMCheck right
engine
1:30 PMCheck left
engine
2:00 PMCheck
stabilizers
2:30 PMGo to Gate 7
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Motivation
3Presenter: Haiming Jin
• Emerging mission-driven workflow-based mobile sensor networks• Airplane maintenance• Industrial production line management• Infrastructure monitoring
Mobile Diagnostic Robot
• Cameras• Microphones• etc.
Railway
Inspection
Pipeline
Inspection
![Page 4: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/4.jpg)
Motivation
4Presenter: Haiming Jin
• Sensory data collection using APs (relays or base stations) • Stationary APs:
• [Huang et al., SECON’10], [Misra et al., ToN’10] and …• Resource overprovisioning!
1:00 PMLocation A
1:30 PMLocation B
2:00 PMLocation C
![Page 5: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/5.jpg)
Motivation
4Presenter: Haiming Jin
• Sensory data collection using APs (relays or base stations) • Stationary APs:
• [Huang et al., SECON’10], [Misra et al., ToN’10] and …• Resource overprovisioning!
• Mobile APs:
1:00 PMLocation A
1:30 PMLocation B
2:00 PMLocation C
![Page 6: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/6.jpg)
Motivation
4Presenter: Haiming Jin
• Sensory data collection using APs (relays or base stations) • Stationary APs:
• [Huang et al., SECON’10], [Misra et al., ToN’10] and …• Resource overprovisioning!
• Mobile APs: • Minimize energy consumption: [Xing et al., Mobihoc’08] and … • Maximize network life time: [Xie et al., Infocom’13] and …• Minimize deployment cost: this paper
![Page 7: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/7.jpg)
Problem Description
5Presenter: Haiming Jin
Objective• Minimize total AP deployment cost
• Purchasing cost (#)• Movement cost (moving distance)
Constraints• Lower bound bandwidth for sensors • Upper bound bandwidth for APs• Moving speed of APs
![Page 8: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/8.jpg)
Model and Assumptions
6Presenter: Haiming Jin
• Mobile users (MUs)•
• Time slots,•
• MUs move according to predefined trajectories• Extracted from workflows
• APs stay only at grid intersections• Move between grid intersections
along shortest paths• Obstacles occlude wireless signal
A
BC
A
B
C
B
AC
D
A
B
C
D
E
Obstacle #1
Obstacle #2
MU1
MU2
MU3
MU4
A
BC
A
B
C
B
AC
D
A
B
C
D
E
Obstacle #1
Obstacle #2
MU1
MU2
MU3
MU4
A
BC
A
B
C
B
AC
D
A
B
C
D
E
Obstacle #1
Obstacle #2
MU1
MU2
MU3
MU4
Obstacle #2
AP1
AP2
AP3
AP4
Obstacle #2
C
A
B
A
BCB
AC
D
A
B
C
D
E
Obstacle #1
Obstacle #2
MU1
MU2
MU3
MU4
AP1
AP2
AP3
AP4
Obstacle #2
C
A
B
A
BCB
AC
D
A
B
D
E
C
Obstacle #1
MU1
MU2
MU3
MU4
Obstacle #2Obstacle #2Obstacle #2
AP1
AP2
AP3
AP4
Obstacle #2
Time Slot tTime Slot t+1
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Mathematical Formulations-Overview
7Presenter: Haiming Jin
MinAD
......CMinWorkflow
Info MinAD
MinAD
Input
Output
......
• Sub-problem I: Minimum AP Deployment (MinAD)• Calculate the minimum number AP deployment in every time slot that satisfies
MUs’ bandwidth requirement
• Sub-problem II: Cost Minimization (CMin)• Given output from MinAD, calculate minimum cost AP deployment
![Page 10: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/10.jpg)
Mathematical Formulations-MinAD
8Presenter: Haiming Jin
MinAD
......
CMinWorkflowInfo MinAD
MinAD
Input
Output
......
• Extract network topology graphs• • Trajectory discretization
1 ...
1 2 3 5 6
2 N
4 7 8 9 10
Candidate AP locations
Network Topology Graph in Time Slot t
A
BC
A
B
C
B
AC
D
A
B
C
D
E
Obstacle #1
Obstacle #2
MU1
MU2
MU3
MU4
A
BC
A
B
C
B
AC
D
A
B
C
D
E
Obstacle #1
Obstacle #2
MU1
MU2
MU3
MU4
1234
5 67
8
9
10A
BC
A
B
C
B
AC
D
A
B
C
D
E
Obstacle #1
Obstacle #2
MU1
MU2
MU3
MU4
1234
5 67
8
9
10
Obstacle #2
AP1
AP2
AP3
AP4
![Page 11: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/11.jpg)
Mathematical Formulations-MinAD
9Presenter: Haiming Jin
MinAD
......
CMinWorkflowInfo MinAD
MinAD
Input
Output
......
Sub-problem I: MinAD
• Variables:• : whether there should be an AP at
location in time slot • : amount of data sent from SU at
position to AP at location in time slot
1 ...
1 2 3 5 6
2 N
4 7 8 9 10
![Page 12: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/12.jpg)
Mathematical Formulations-MinAD
9Presenter: Haiming Jin
MinAD
......
CMinWorkflowInfo MinAD
MinAD
Input
Output
......
Sub-problem I: MinAD
• Objective:• Minimize the number of APs
• Constraints:• Lower bound bandwidth for sensors • Upper bound bandwidth for APs
1 ...
1 2 3 5 6
2 N
4 7 8 9 10
![Page 13: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/13.jpg)
Mathematical Formulations-CMin
10Presenter: Haiming Jin
MinAD
......
CMinWorkflowInfo MinAD
MinAD
Input
Output
......
AP Position Transition Graph
Sub-problem II: CMin
• AP purchasing cost
1
2
3
2
1
2
3
1
3
1
2
3
t=1 t=2 t=3 t=4
![Page 14: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/14.jpg)
Mathematical Formulations-CMin
10Presenter: Haiming Jin
AP Position Transition Graph
Sub-problem II: CMin
• Total moving cost
1
2
3
2
1
2
3
1
3
1
2
3
t=1 t=2 t=3 t=4
MinAD
......
CMinWorkflowInfo MinAD
MinAD
Input
Output
......
![Page 15: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/15.jpg)
Mathematical Formulations-CMin
10Presenter: Haiming Jin
AP Position Transition Graph
Sub-problem II: CMin
• Total AP deployment cost
1
2
3
2
1
2
3
1
3
1
2
3
t=1 t=2 t=3 t=4
1
2
3
2
1
2
3
1
3
1
2
3
t=1 t=2 t=3 t=4
1
2
3
2
1
2
3
1
3
1
2
3
t=1 t=2 t=3 t=4
MinAD
......
CMinWorkflowInfo MinAD
MinAD
Input
Output
......
![Page 16: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/16.jpg)
Solution and Analysis-NP-hardness
11Presenter: Haiming Jin
Theorem 1: The MinAD problem is NP-hard.
Proof: We prove the NP-hardness of the MinAD problem by showing that the set cover problem (NP-complete) is polynomial time reducible to MinAD.
Theorem 2: The CMin problem is NP-hard.
Proof: We prove the NP-hardness of the CMin problem by showing that the minimum cost three dimensional perfect matching problem (NP-complete) is polynomial time reducible to CMin.
![Page 17: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/17.jpg)
Solution and Analysis-Approximation Algorithm
12Presenter: Haiming Jin
Linear programming relaxation and iterative rounding (LR-IR)
![Page 18: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/18.jpg)
Solution and Analysis-Approximation Algorithm
13Presenter: Haiming Jin
Theorem 3: LR-IR for MinAD has linear approximation ratio w.r.t. maximum node degree of the network connectivity graph.
Theorem 4: LR-IR for CMin has constant approximation ratio.
![Page 19: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/19.jpg)
Performance Evaluation
14Presenter: Haiming Jin
Simulation Settings
![Page 20: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/20.jpg)
Performance Evaluation
14Presenter: Haiming Jin
Scenario I Scenario II
![Page 21: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/21.jpg)
Performance Evaluation
15Presenter: Haiming Jin
LR-IR for MinAD LR-IR for CMin
![Page 22: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/22.jpg)
Conclusion
15Presenter: Haiming Jin
• We formulate the cost-minimizing mobile AP deployment problem as meaningfully solvable (mixed) integer optimization problems and prove that the formulated optimization problems are NP-hard.
• Further, we design efficient approximation algorithms with guaranteed approximation ratios.
![Page 23: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/23.jpg)
Thank you !
![Page 24: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/24.jpg)
Backup Slides
![Page 25: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/25.jpg)
Incomplete Information Workflows
18Presenter: Haiming Jin
• Durations that MUs stay at mission locations are not a priori known.
• Shared-AP trajectory• Stationary APs
• Dedicated-AP trajectory• Mobile APs
......
TrajectoryInfo
MinAD
Input
Output
......
Trajectory Selection
CMinInC
......
MinAD CMinInC
MinAD CMinInC
![Page 26: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/26.jpg)
Performance Evaluation
19Presenter: Haiming Jin
Percentage of Selected Trajectory Segments
![Page 27: Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d1a5503460f949ef25b/html5/thumbnails/27.jpg)
Performance Evaluation
20Presenter: Haiming Jin