1. Dimitrios Katsaros* † Yannis Manolopoulos* † Aristotle University, Greece *University of Thessaly, Greece Suffix Tree Based Prediction for Pervasive Computing Environments

2. Panhellenic Conference on Informatics, 11-13 November 2005 2 The architecture of a PCS

3. Panhellenic Conference on Informatics, 11-13 November 2005 3 Information dissemination in a PCS Information System (server) Wireless Cell Base Station Downlink Communication Bandwidth Mobile Hosts (MH) #MHosts >> #Servers Uplink bandwidth << Downlink bandwidth

4. Panhellenic Conference on Informatics, 11-13 November 2005 4 Roaming: Where is the mobile? The mobile can freely roam inside the coverage area of the cellular system Arises the need for location management –location update –location prediction

5. Panhellenic Conference on Informatics, 11-13 November 2005 5 Querying: What data will be requested? The mobile can request any data available in the information system Arises the need for –Proactively pushing them into the broadcast channel –Proactively sending them to the next-to-visit base station

6. Panhellenic Conference on Informatics, 11-13 November 2005 6 Predict: Position & Information Needs Why is the location prediction useful? –effective solutions to the mobility tracking/prediction problem can reduce update and paging costs, freeing the network from excessive signaling traffic [bd02]. Why is the request prediction useful? –Accurate data request prediction results in effective prefetching [nkm03], which combined with a caching mechanism [km04], can reduce user-perceived latencies as well as server and network loads [bd02] A. Bhattacharya and S. K. Das, LeZi-Update: An information-theoretic framework for personal mobility tracking in PCS networks, ACM/Kluwer Wireless Networks, 8(2-3), pp. 121 – 135, 2002. [nkm03] A. Nanopoulos, D. Katsaros, Y. Manolopoulos, A data mining algorithm for generalized Web prefetching, IEEE Transactions on Knowledge and Data Engineering, 15(5), pp. 1155 – 1169, 2003. [km04] D. Katsaros and Y. Manolopoulos, Web caching in broadcast mobile wireless environments, IEEE Internet Computing, 8 (3), pp. 37 – 45, 2004.

7. Panhellenic Conference on Informatics, 11-13 November 2005 7 Where is prediction based? Both of the aforementioned problems are related to the ability of the underlying network to –record, –learn and, subsequently –predict the mobile's “behaviour”, i.e., its movements or its information needs The success of the prediction is presupposed and is boost by the fact that mobile users exhibit some degree of regularity in their movement and/or in their access patterns This regularity may be apparent in the behaviour of each individual client or in client groups.

8. Panhellenic Conference on Informatics, 11-13 November 2005 8 Location prediction  Request prediction These issues had been treated in isolation, but pioneering works ([vk96] and [bd02]) are paving the way for treating both problems in an homogeneous fashion Use methods for data compression (thus, characterized as “information-theoretic”), in carrying out prediction. They model the respective state space as finite alphabets comprised of discrete symbols In the mobility tracking scenario, the alphabet consists of all possible sites (cells) where the client has ever visited or might visit (assuming that the number of cells in the coverage area is finite) In the request prediction scenario, the alphabet consists of all the data objects requested by the client plus the objects that might be requested in the future (assuming that the objects come from a database and thus their number is finite) [vk96] J. S. Vitter and P. Krishnan, Optimal prefetching via data compression, Journal of the ACM, 43 (5), pp. 771–793, 1996.

9. Panhellenic Conference on Informatics, 11-13 November 2005 9 4 Families of predictors PPM: Prediction by Partial Match LZ78: Lempel-Ziv 1978 PST: Probabilistic Suffix Tree CTW: Context –Tree Weighting Overheads FamilyTrainingParameterizationStorage LZ78 Onlinemoderate PPM online/offlinemoderate/heavylarge PST offlineheavylow CTW onlinemoderatelarge

10. Panhellenic Conference on Informatics, 11-13 November 2005 10 The PPM predictor Running sequence: aabacbbabbacbbc

11. Panhellenic Conference on Informatics, 11-13 November 2005 11 The LZ78 predictor Running sequence: aabacbbabbacbbc Enhanced

12. Panhellenic Conference on Informatics, 11-13 November 2005 12 The PST predictor Running sequence: aabacbbabbacbbc

13. Panhellenic Conference on Informatics, 11-13 November 2005 13 The CTW predictor (1/3) Running bin sequence: 010|11010100011 Krichevsky-Trofimov estimator:

14. Panhellenic Conference on Informatics, 11-13 November 2005 14 The CTW predictor (2/3)

15. Panhellenic Conference on Informatics, 11-13 November 2005 15 The CTW predictor (3/3)

16. Panhellenic Conference on Informatics, 11-13 November 2005 16 Discrete Sequence Prediction Problem At any given time instance t (meaning that t symbols x t, x t-1,...,x 1 have appeared, in reverse order) calculate the conditional probability where This model introduces stationary Markov chain, since the probabilities are not time-dependent The outcome of the predictor is a ranking of the symbols according to their P. The predictors which use such kind of prediction models are termed Markov predictors

17. Panhellenic Conference on Informatics, 11-13 November 2005 17 The STP algorithm [em92] A. Ehrenfeucht and J. Mycielski, A pseudorandom sequence – How random is it?, American Mathematical Monthly, 99 (4), pp. 373–375, 1992.

18. Panhellenic Conference on Informatics, 11-13 November 2005 18 An example execution of STP Suppose that the sequence of symbols seen so far is the following: s 1 24 = abcdefgabcdklmabcdexabcd$ The largest suffix of s 1 24 which appears somewhere in s 1 24 is the ss 1 4 = abcd Let α = 0.5 Then sss 1 2 = cd The appearances of cd inside s 1 24 are located at the positions 3, 10, 17, 23 Therefore, the marked positions are the 5, 12, 19, 25 The last one is NULL since it contains the symbol we want to predict Thus, the sequence of candidate predicted symbols is e,k,e. Since the symbol that appears most of the times in this sequence is the e, the output of the STP algorithm, i.e., the predicted symbol at this stage, is e.

19. Panhellenic Conference on Informatics, 11-13 November 2005 19 An example execution of STP Suppose that the sequence of symbols seen so far is the following: s 1 24 = abcdefgabcdklmabcdexabcd$ The largest suffix which appear somewhere is the seq is abcd, and s 1 24 = abcdefgabcdklmabcdexabcd$ Let α = 0.5, thus we use a portion of abcd, half of it: cd Appearances of cd in the sequence are: s 1 24 = abcdefgabcdklmabcdexabcd$ Candidate predictions Since e appears most of the times, the final outcome of the prediction is: e

20. Panhellenic Conference on Informatics, 11-13 November 2005 20 Proof of concept of STP (1/2) Definition. The ratio of symbols returned by the predictor that indeed match with the next event/symbol in the sequence, divided by the total number of symbols return by the predictor defines the prediction precision

21. Panhellenic Conference on Informatics, 11-13 November 2005 21 Proof of concept of STP (2/2) Definition. The total number of symbols return by the predictor divided by the total number of events/symbols of the sequence defines the prediction overhead

22. Panhellenic Conference on Informatics, 11-13 November 2005 22 Thank you for your attention! Any questions ?