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Skyline Charuka Silva. Outline Charuka Silva, Skyline2  Motivation  Skyline Definition  Applications  Skyline Query  Similar Interesting Problem.

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Presentation on theme: "Skyline Charuka Silva. Outline Charuka Silva, Skyline2  Motivation  Skyline Definition  Applications  Skyline Query  Similar Interesting Problem."— Presentation transcript:

1 Skyline Charuka Silva

2 Outline Charuka Silva, Skyline2  Motivation  Skyline Definition  Applications  Skyline Query  Similar Interesting Problem  Algorithms  Divide and Conquer Algorithm  Index based Algorithm  Nearest Neighbor

3 Trip to Nassau (Bahamas)  Hotel that is cheap and close to the beach.  Two goals are complementary as the hotels near the beach tend to be more expensive.  Travel agent can suggest all interesting hotels.  Interesting are all hotels that are not worse than any other hotel in both dimensions.  We call this set of interesting hotels the Skyline Charuka Silva, Skyline3

4 Distribution of Hotels Charuka Silva, Skyline4

5 Formal Skyline Definition Skyline is defined as those points which are not dominated by any other point. A point dominates another point if it is as good or better in all dimensions and better in at least one dimension. Charuka Silva, Skyline5

6 Where It Applies? Skyline operator is important for applications involving multi- criteria decision making. Charuka Silva, Skyline6

7 Some Applications  Customer information systems, travel agencies and mobile city guides. Skyline has to be computed as user move on.  The Skyline of Manhattan, for instance, can be computed as the set of buildings which are high and close to the Hudson river.  Decision Support (Business intelligence), e.g. Customers who buy more and complain little  Data visualization. E.g. The points of an object from certain perspective can be determined  Distributed Query optimization. E.g. find set of interesting sites which have high computation power and are close to data needed to execute the query. Charuka Silva, Skyline7

8 Skyline Query select * from Hotels, skyline of price min, distance min what else: max, joins, group by and so on. Charuka Silva, Skyline8

9 Skyline Query Results Results for the query will be {a,i,k} Charuka Silva, Skyline9

10 Top-K Queries Vs Skyline  Top-K (or ranked) queries retrieve the best K objects that minimize a specific preference function.  E.g. Given preference function f(x,y)=x+y, the top-3 query  Retrieves,, (in this order) Charuka Silva, Skyline10

11 Divide-and-Conquer (D&C)  Divides the dataset into several partitions so that each partition fits in memory  The partial skyline of the points in every partition is computed  Merge the partial ones to obtain full skyline Algorithm 1 ‏ Charuka Silva, Skyline11

12 { a,c,g}, {d}, {i},{m,k} Partitioned Space Charuka Silva, Skyline12

13 Divide and Conquer  All points in the skyline of s 3 must remain.  Those in s 2 are discarded; dominated by s 3  Each skyline point in s 1 is compared only with points in s 3, no point in s 2 or s 4 can dominate those in s 1. Charuka Silva, Skyline13

14 Drawbacks  D&C efficient only for small data sets. If the data set is large, the partitioning process requires reading and writing entire data set at least once : high I/O cost  Not suitable for online applications: can't report any results until partition process completes. Charuka Silva, Skyline14

15 Index Based Skyline  Organize set of d-dimensional points into d lists, a point p = (p1, p2,..., pd) is assigned to the ith list (1≤i≤d) when pi is the smallest.  Points in each list are sorted in ascending order of their minimum  A batch in the ith list consists of points that have the same ith coordinate Algorithm 2 Charuka Silva, Skyline15

16 Index List Charuka Silva, Skyline16

17 Processing a batch  Computing the skyline inside the batch  Among the computed points, it adds the ones not dominated by any of the already-found skyline points into the skyline list Charuka Silva, Skyline17

18 Processing a batch  Loads the first batch of each list, and handles the one with the minimum minC ( i.e. {a}, {k} ), add {a} to the Skyline list  Compare batch {b} and {k}, and add {k} to the list.  Load {b} and {i,m} ; Find skyline inside {i,m} first, that is {i}  Compare {i} and {b} and add {i} to skyline list  Algorithm stops, since any other batch is greater than or equal to {i}  Skyline is {a,k,i} Charuka Silva, Skyline18

19 Pros and Cons  Hashing technique is straight forward and incurs low CPU overhead  But high I/O cost, since multiple queries access large part of space.  Propagate and merge incur high I/O cost to scan to-do lost every time when a point is discovered and when finding best fit to merge. Charuka Silva, Skyline19

20 Nearest Neighbor (NN)  Performs a NN query on the R-tree, to find the point with the minimum distance from the beginning of the axes (point o).  Distances are computed according to L1 norm  All the points in the dominance region are exempt from further consideration  Results of NN search is used to partition the data universe recursively. Algorithm 3 Charuka Silva, Skyline20

21 Nearest Neighbor (NN) Two Partitions [0,i x ) [0,∞) and (ii) [0,∞) [0,i y ) Partition1: 1, 3 Partition2: 1,2 Charuka Silva, Skyline21

22 Nearest Neighbor (NN)  The set of partitions resulting after the discovery of a skyline point are inserted in a to-do list  While the to-do list is not empty, NN removes one of the partitions from the list and recursively repeats the same process Charuka Silva, Skyline22

23 Nearest Neighbor (NN) [ 0,a x ) [0,∞) subdivisions 1 and 3 [0,i x ) [0,a y ) subdivision 1 and 2 Charuka Silva, Skyline23

24 NN Concepts  Laisser-faire: A main memory hash table stores the skyline points found so far.  Propagate: When a point p is found, all the partitions in the to- do list that contain p are removed and re-partitioned according to p.  Merge: The main idea is to merge partitions in the to-do, thus reducing the number of queries that have to be performed.  Fine-grained Partitioning: The original NN algorithm generates d partitions after a skyline point is found. An alternative approach is to generate 2d non-overlapping subdivisions. Charuka Silva, Skyline24

25 Reference  S. Borzs onyi, D. Kossmann, and K. Stocker.The skyline operator. In Proc. IEEE Conf. on Data Engineering, Heidelberg, Germany, 2001.  K.-L. Tan, P.-K. Eng, and B. C. Ooi. Ecient progressive skyline computation. In Proc. of the Conf. on Very Large Data Bases, Rome, Italy, Sept. 2001  H. T. Kung, F. Luccio, and F. P. Preparata.On finding the maxima of a set of vectors. Journal of the ACM, 22(4), 1975  Kossmann, D., Ramsak, F., Rost, S. Shooting Stars in the Sky: an Online Algorithm for Skyline Queries.VLDB, 2002.  Dimitris Papadias, Yufei Tao, Greg Fu Bernhard Seeger. An optimal and progressive algorithm for skyline queries. In Conf. on Management of Data ACM SIGMOD 2003. Charuka Silva, Skyline25

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