CHAPTER 18 Distributed Network and System Monitoring 477 18.5. SUMMARY AND FUTURE DIRECTIONS For a distributed monitoring system, the NOC needs to collect data from multiple locations and detect any events of interest in a real-time man- ner. In this chapter, we first provide an overview of the information aggregation problem in the data stream computation. We mainly focus on recent efficient algorithm in the sliding window model, which can provide a fresh and up-to-date view of the CPI system. Next, we discussed sev- eral challenges in a distributed monitoring sys- tem. In this case, we want to find patterns among multiple data streams and compare the differ- ences among them. Also, we need to handle the data transportation delays and costs in a dis- tributed monitoring system. 7. Given two data streams, i.e., x 1 , x 2 , . . . , x i , . . . and y 1 , y 2 , . . . , y i , . . . , could you find an item which does not appear in both data streams? Could you find an item which only appears in the first data stream? REFERENCES [1] S. Muthukrishnan, Data streams: algorithms and applications, Found. Trends Theor. Comput. Sci. 1 (2) (2005) 117­236. [2] C.C. Aggarwal, Data Streams: Models and Algorithms (Advances in Database Systems), Springer-Verlag New York, Inc., Secaucus, NJ. [3] M. Datar, A Gionis, P. Indyk, R. Motwani, Maintaining stream statistics over sliding windows: (extended abstract), in: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '02, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2002, pp. 635­644. [4] B. Babcock, M. Datar, R. Motwani, L.