Distributed Geometric Data Structures. Philip Levis Stanford Platform Lab Review Feb 9, 2017
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1 Distributed Geometric Data Structures Philip Levis Stanford Platform Lab Review Feb 9, 2017
2 Big Control
3 The Physical World Big control applications collect data on, and take action in, the physical world There will be a lot of data: they need distributed data structures to store, query, and compute on it Big control applications have high locality (literally) Physical world data is geometric (2D, 3D) in nature; it has much more complex data inter-dependencies than key-value stores Need new, distributed geometric data structures
4 Outline Example big control applications Geometric data structures Distributing geometric data structures
5 Outline Example big control applications Geometric data structures Distributing geometric data structures
6 Disaster Response
7
8
9
10 Beverages Child
11 Data Requirements Altitude produces different data resolutions Dynamically changing in response to application actions Data changes/decays over time: 4D Grid-based (e.g., temperature, pixels) as well as pointbased data (people, objects, landmarks)
12 Outline Example big control applications Geometric data structures Distributing geometric data structures
13 Two Basic Approaches X A Z B C Y D A X B Z C Y D A C D F B E G Z A B C Y D E F G geometry data structure geometry data structure Bounding Volume Hierarchy (BVH) Spatial subdivision
14 Two Basic Approaches X A Z B C Y D A X B Z C Y D A C D F B E G Z A B C Y D E F G geometry data structure geometry data structure Bounding Volume Hierarchy (BVH) Spatial subdivision
15 Spatial subdivision Many variants: quad/oct-trees, kd-trees, binary space partitioning Oct-tree: subdivide each axis evenly
16 Problem with Oct-trees Sparse, pointer structure: low locality, cache-poor
17 Another Problem 1,000-fold resolution increase 30-fold altitude increase Level Many levels for large variations in resolution
18 VDB (Museth, ACM TOG 2013 Vol 32, 3:27) Hierarchical data structure for the efficient representation of sparse, time-varying volumetric data discretized on a 3D grid fold 2 3 = 2 12
19 VDB (Museth, ACM TOG 2013 Vol 32, 3:27) Hierarchical data structure for the efficient representation of sparse, time-varying volumetric data discretized on a 3D grid 2 5 Single host fold 2 3 = 2 12
20 Outline Example big control applications Geometric data structures Distributing geometric data structures
21 ?
22 Problem 1: Distribution Where should the system place each tree node? Option 1: Random/spray placement Improves potential read bandwidth Balances load easily Option 2: Locality-based placement Better when computations pushed to data (granular computing) Load balancing is an open problem Strawman: balance data size (assumes uniform computation)
23 Problem 2: Not So Simple Staggered (MAC) grids store data on faces as well as in cells: important to represent flow fij fij cij
24 Problem 2: Not So Simple Staggered (MAC) grids store data on faces as well as in cells: important to represent flow cij -temperature, burn state, etc. fij - wind
25 Problem 2: Not So Simple Staggered (MAC) grids store data on faces as well as in cells: important to represent flow cij - # of people fij - movement of people
26 Problem 2: Not So Simple Cell and face values should have locality Distributed grids require replication ( ghost cells ) Minimizing surface area of volumes minimizes communication, but complicates load balancing fij fij cij
27 Problem 3: Dynamic Updates Applications will dynamically subdivide and coarsen the data structure Operations may trigger load rebalancing: need to mask latency from application (asynchrony/ replication)
28 Problem 4: Time Big control applications require being able to look backwards in time Where did those people needing rescue go? Where did the fire jump the fire break? What is traffic downtown like in 15 minutes (at 5:30PM)? Complicates load balancing: historical data should be close to current data
29 Current Status Understanding bottlenecks/performance issues requires workloads (computations, hierarchy structure) Have implemented multi-resolution FLIP simulation Next step: simulator for drone exploration Integrating replication/ghost cells for distribution
30 Conclusion Big control applications use geometric data structures Dynamically distributing these data structures is an open problem We re starting with space partitioning (have some prior results on BVHs) Chinmayee Shah
31 Hilbert Helix
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