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

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

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

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

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

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

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

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

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Obstacle #1

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Time Slot tTime Slot t+1

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

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

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1234

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AP1

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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

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

Mathematical Formulations-CMin

10Presenter: Haiming Jin

MinAD

......

CMinWorkflowInfo MinAD

MinAD

Input

Output

......

AP Position Transition Graph

Sub-problem II: CMin

• AP purchasing cost

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t=1 t=2 t=3 t=4

Mathematical Formulations-CMin

10Presenter: Haiming Jin

AP Position Transition Graph

Sub-problem II: CMin

• Total moving cost

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MinAD

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CMinWorkflowInfo MinAD

MinAD

Input

Output

......

Mathematical Formulations-CMin

10Presenter: Haiming Jin

AP Position Transition Graph

Sub-problem II: CMin

• Total AP deployment cost

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MinAD

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CMinWorkflowInfo MinAD

MinAD

Input

Output

......

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.

Solution and Analysis-Approximation Algorithm

12Presenter: Haiming Jin

Linear programming relaxation and iterative rounding (LR-IR)

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.

Performance Evaluation

14Presenter: Haiming Jin

Simulation Settings

Performance Evaluation

14Presenter: Haiming Jin

Scenario I Scenario II

Performance Evaluation

15Presenter: Haiming Jin

LR-IR for MinAD LR-IR for CMin

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.

Thank you !

Backup Slides

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

Performance Evaluation

19Presenter: Haiming Jin

Percentage of Selected Trajectory Segments

Performance Evaluation

20Presenter: Haiming Jin