SASB: Spatial Activity Summarization using Buffers

Atanu Roy & Akash Agrawal

Overview

• Motivation• Problem Statement• Computational Challenges• Related Works• Approach• Examples• Conclusion

Motivation

• Applications in domains like

– Public safety

– Disaster relief operations

SASB

SASB Problem Statement• Input

– A spatial network,– Set of activities & their location in space,– Number of buffers required (k),– A set of buffer (β),

• Output– A set of k active buffers, where

• Objective– Maximize the number of activities covered in the k buffers

• Constraints– Minimize computation costs

Definitions

• Constant Area Buffers– Node buffers

– Path buffers

Running Example

Coverage

Path Buffer = 16 Node Buffer = 15 Total Coverage = 31/33

Computational Challenges

• SASB is NP-Hard• Proof:

– KMR is a special case of SASB • Buffers have width = 0

– KMR is proved to be NP-Complete– SASB is at least NP-Hard

Related Works

Geometry basedNo Yes

Network based

YesPath based:

KMR, Mean Streets

0-1 Subgraph:SANET, Max Subgraph

This work

No-

K-Means, K-Medoids, P-median,

Hierarchical Clustering

Contributions

• Definition SASB problem • NP-Hardness proof• Combination of geometry and network based

summarization.• First principle examples

Greedy Approach

Choice of k-best buffers

• Repeat k times– Choose the buffer with maximum activities – Delete all activities contained in the chosen buffer from all the

remaining buffers– Replace the chosen buffer from buffer pool to the result-set

Execution Trace

NB_A = 8

NB_B = 6

NB_C = 11

PB_1 = 8

PB_2 = 12

PB_12 = 2

NB_A = 8 NB_A = 8

NB_B = 6 NB_B = 2

NB_C = 11 NB_C = 1

PB_1 = 8 PB_1 = 7

PB_2 = 12 PB_2 = NA

PB_12 = 2 PB_12 = 1

Execution Trace: Final Solution

Best Case Scenario

Type Coverage Rank

Total 33 NA

Geo 27 2

N/w 14 3

SASB 31 1

Better

Type Coverage Rank

Total 14 NA

Geo 9 3

N/w 11 2

SASB 14 1

Average Case Scenario

Type Coverage

Rank

Geo 10 3

N/w 10 2

SASB

1

Type Coverage Rank

Total 10 NA

Geo 8 2

N/w 10 1

SASB 10 1

Conclusion

• Provides a framework to fuse geometry and network based approaches.

• First principle examples indicates it can be comparable with related approaches.

Acknowledgements

• CSci 8715 peer reviewers who gave valuable suggestions.

Thank you