Efficient Spatial Sampling of Large Geographical Tables

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Efficient Spatial Sampling of Large Geographical Tables (SIGMOD ‘12 / TODS ‘13) Anish Das Sarma, Hongrae Lee, Hector Gonzalez, Jayant Madhavan, Alon Halevy Google Research Presented by Emaad Ahmed Manzoor March 10, 2014

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Thinning

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Constraints Objectives Challenges

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Definitions

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Definitions

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Visibility Zoom Consistency Adjacency Constraints

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The Thinning Problem

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K = 1 M1 = { 4, 4, 4, 4, 4 } M2 = { 1, 3, 4, 4, 4 } M3 = { 2, 3, 4, 4, 4 }

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Maximality Fairness Importance Objectives

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K = 1 M1 = { 4, 4, 4, 4, 4 } M2 = { 1, 3, 4, 4, 4 } M3 = { 2, 3, 4, 4, 4 }

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Problem Maximality Fairness Importance Visibility Zoom Consistency Adjacency Constraints Objectives

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Problem Maximality Fairness Importance Visibility Zoom Consistency Adjacency Constraints Objectives Optimization

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Integer Programming

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Variables

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Sampling Constraints

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Zoom Consistency & Visibility Constraints

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Thinning solution

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Program Size

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Critical nodes

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Bounded Cover

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Critical nodes

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Program Size

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Relaxing Integer Constraints

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Objectives

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Maximality

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Strong Maximality There does not exist M’ such that:

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K = 1 M1 = { 4, 4, 4, 4, 4 } M2 = { 1, 3, 4, 4, 4 } M3 = { 2, 3, 4, 4, 4 } M4 = { 1, 4, 4, 4, 3 }

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Strong Maximality is NP-Hard

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Weak Maximality There does not exist M’ such that: for some 1 <= i <= n

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K = 1 M1 = { 4, 4, 4, 4, 4 } M2 = { 1, 3, 4, 4, 4 } M3 = { 2, 3, 4, 4, 4 } M4 = { 1, 4, 4, 4, 3 }

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DFS

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K = 1 M2 = { 1, 3, 4, 4, 4 }

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Point-only Datasets

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Experiments

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2.67GHz quad-core 12GB (starting at 1GB, or 4GB for the scalability tests) Java 1.6 Apache Simplex K=500 “Some plots were too big, so we threw them out.”

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Program Size

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Integer Relaxation

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Scalability

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Objectives

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Takeaways

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Use DFS if you care only about maximality Otherwise use the minimised LP The randomized points-only algorithm consumes constant memory and scales arbitrarily (not shown)