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Continuous Monitoring of Nearest Neighbors on Land Surface. Presented by Ivan Chiou. Authors. Computer science department university of Southern California Los Angeles. Songhua Xing a PhD candidate at Computer Science Department now at IBM T.J. Watson Research Center - PowerPoint PPT Presentation
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Continuous Monitoring of Nearest Neighbors on
Land Surface
Presented by Ivan Chiou
AuthorsComputer science department university of Southern California Los Angeles.
Songhua Xinga PhD candidate at Computer Science Departmentnow at IBM T.J. Watson Research CenterCountry: China
Cyrus ShahabiDirector of the Information Laboratory (InfoLAB)Professor of Computer Science and Electrical Engineering at USC Director of the Integrated Media Systems CenterChief Technology Officer and Founder of Geosemble TechnologiesPh.D. in Computer Science
Bei Pana PhD candidate at Computer Science Department
Microsoft Research Asia, Autodesk, University of Southern California
Country:China
AbstractNew type kNN queries
Surface k Nearest Neighbor(skNN) queries Extend to constrained third dimension
Two exact methods for highly dynamic environment as arbitrary movement
SE(Surface Expansion)-TreeFat and short - not efficiency an analogous counterpart of the Dijkstra Expansion Tree on land surface
ASI(Angular Surface Index)-TreeThin and tall – low cpu and I/O overhead
IntroductionRelated research
Static and dynamic query
Problem & PreliminarieskNN methods only on Euclidean and road networks.skNN is for surface distance, represented as triangular meshes. CskNN can be used on continuous queries and the complexities of land surfaces.
CskNN algorithmmonitor and coordinate among the moving objects.One of CkNN for road map
Dijkstra Expansion treeSE-Tree – for Static query
More effective – ASI-Tree
Details of our surface index(ASI) and its corresponding CskNNDynamic query
ExperimentsSummary and future work
ASI- Tree outperforms SE-Tree
Related worksStatic(snapshot) query
Different constrained environmentRoad networksLand surface
Dynamic query The paper three types of updates
Object movementsQuery movementsFluctuations of edge weights
PreliminariesAssumption and problem definition
Moving objectPoint Of Interest
Static query pointThree distance metrics
Euclidean distanceLower bound of surface distance
Network distanceUpper bound of surface distance
Surface distance
PreliminariesProblem definition
query consists of two stepssnapshot skNN querycontinuously monitoring and updating the result sets as the objects move
PreliminariesShortest surface path computation
Chen-Han algorithm costs Unfolding process - expensive
PreliminariesSurface expansion tree
Dijkstra Expansion tree, based on the Chen-Han algorithmDefinition
Surface Expansion Tree is the final result of Chen-Han algorithm and there is only one path from the source to the vertice
PreliminariesSurface expansion tree
Preliminaries - observation
Preliminaries - observation
Observation 1 makes partitioning these surface shortest paths of an SE-Tree possible.
Observation 2 DrawbackSE-Tree in general is fat and short
Naive approachSurface Expansion Tree
Initial query processing – two areas
Object movementsThree categories
Within the result boundary
Ignore this caseResult set remains the same
Incoming movementOutgoing movement
Two scenariosMore Outgoing movementMore Incoming movement
Naïve algorithmExpansion phase, the complexity is In the shrinking phase, there is no surface distance computation
Complexity is mlog(m)
Analysis – Expansion & Shrink
SimilarityAll these methods built an expansion tree rooted at the query pointThe result boundary and expansion boundary are the same on road networks.
DifferentThis naïve approach could be fast during the phase when the SE-Tree shrinksExpansion Two problems:
Surface path computation is extremely highExpansion areas of SE-Tree could be large.
Overcome by Surface Shortest Path Container store partial results of pre-computationbuild a novel index schema(Angular Surface Index(ASI))
SURFACE INDEX BASED ALGORITHM(1/2)
Angular Surface Index (ASI)Thin and tallTwo data structure
Surface Shortest Path ContainerSurface Equidistant Line
SURFACE INDEX BASED ALGORITHM(2/2)
Surface Shortest Path ContainerTo pre-compute a complete SE-Tree offline and store its shortest path.Two Steps
locate the data object using a spatial indexretrieve the shortest path directly from disk
Drawbacksa data object lays on the face rather than a vertex, this approach cannot find the exact shortest path and the accurate distancestoring all these shortest paths is per siteThe search time is almost linear.
How to speed uptake advantage of partial results based on geometric property to speed up the online process.
Surface Shortest Path Container(1/4)
The advantage is to minimize the search area of Dijkstra algorithm.A new concept of Cover Set and redefine the concept of Shortest Path Container for surface, and then discuss their spatial properties.
Surface Shortest Path Container(2/4)
According to Observation 1, we can always find a polyline sp from the source s to a point p on the margin of T, which is immediately left to the leftmost shortest path to CS(e) and do not cross any shortest paths, hence sp constitutes the left part of the boundary b.
Surface Shortest Path Container(3/4)
Container’s boundary consists ofthe left boundary line,the right boundary linethe end boundary line (which only exists if the left and right boundary lines do not converge)
Surface Shortest Path Container(4/4)
Creating Surface Shortest Path Container
Propose an algorithm to create a surface shortest path container
Creating Surface Shortest Path Container
In Line 6, the end boundary can be NULL if left and right boundaries do not intersect the margin.The time complexity of Algorithm 3 is O(NlogN) due to the sort operation in Line 3. However, since the pre-computation of shortest paths takes , the overall time complexity is .
Surface Equidistant LineDesigned to partition along the horizontal (latitude) directionThese lines are sorted by their increasing distance value to the source point and this order is termed as levels
Angular Surface Index(1/3)
Based on surface shortest path containers and surface equidistant linesEach partition of is called a surface chunk.With this ASI-Tree, each node represents a container.Compared with SE-Tree, ASI-Tree has the following advantages
Angular Surface Index(2/3)
Angular Surface Index(3/3)
CskNN Query Processing(1/2)
CskNN Query Processing(2/2)
PERFORMANCE EVALUATION(1/6)
Experiment setupModel
BH: Bearhead (BH) area in WA, USA which covers an area around 10.7km×14km and 2)EP: Eagle Peak (EP) area in WY, USA with similar size as BH.Create five synthetic surface models with the same size (10km×10km)
Device PC with Intel 6420 Dual CPU 2.13G Hz and 3.50 GB RAMThe operating system is Windows XP SP2
The parameters100 CskNN queries, each query is 50 timestamps.The first 6 parameters are tested on both BH and EP (Surface Roughness RA is only for synthetic data sets.)
PERFORMANCE EVALUATION(2/6)
The Impact of kASI based algorithm outperforms the naïve algorithm both in query efficiency and I/O operations (least a factor of two for k > 4.)Performance in I/O by an average factor of two because the search is localized to avoid unnecessary access to surface vertices.
PERFORMANCE EVALUATION(3/6)
Uniform or Gaussian distributionsthe ASI based algorithm has a slightly better performance for objects with Gaussian distribution than objects with uniform distribution.
PERFORMANCE EVALUATION(4/6)
The Impact of Object Distribution and DOBoth query processing time and I/O cost decrease for both algorithms as DO increases.
PERFORMANCE EVALUATION(5/6)
The Impact of a and v(a)(b)both query processing time increases slightly as well because the possibility to enlarge the search area is increased.(c)(d)both algorithms are practically unaffected by object speed because the core of both algorithms only concern whether there are object updates rather than how far the objects move.
PERFORMANCE EVALUATION(6/6)
The Impact of DCthe performance is enhanced as more containers are created for both BH and EP.
The Impact of RAASI-based algorithm keeps outperforming the naïve Algorithmrougher terrains could probably generate a larger search area than smooth terrains.
ConclusionPropose two algorithm
naïve algorithmsurface index (ASI) based algorithm
ASI-based algorithm outperforms the naïve algorithm under all circumstances
Simplified problem setting (pre-defined static query points)
Future workFurther studying these complex settings, where queries move arbitrarily.
BACKUP
Presented by Ivan Chiou