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.

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Presented by Ivan Chiou