Spatially-decaying aggregation over a network

Data items are often associated with a location in which they are present or collected, and their relevance or influence decays with their distance. Aggregate values over such data thus depend on the observing location, where the weight given to each item depends on its distance from that location. We term such aggregation spatially-decaying. Spatially-decaying aggregation has numerous applications: Individual sensor nodes collect readings of an environmental parameter such as contamination level or parking spot availability; the nodes then communicate to integrate their readings so that each location obtains contamination level or parking availability in its neighborhood. Nodes in a p2p network could use a summary of content and properties of nodes in their neighborhood in order to guide search. In graphical databases such as Web hyperlink structure, properties such as subject of pages that can reach or be reached from a page using link traversals provide information on the page. We formalize the notion of spatially-decaying aggregation and develop efficient algorithms for fundamental aggregation functions, including sums and averages, random sampling, heavy hitters, quantiles, and L"p norms.

[1]  Jon M. Kleinberg,et al.  Protocols and impossibility results for gossip-based communication mechanisms , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[2]  Srikanta Tirthapura,et al.  Estimating simple functions on the union of data streams , 2001, SPAA '01.

[3]  Jessica H. Fong,et al.  An Approximate Lp Difference Algorithm for Massive Data Streams , 1999, Discret. Math. Theor. Comput. Sci..

[4]  Flip Korn,et al.  Influence sets based on reverse nearest neighbor queries , 2000, SIGMOD 2000.

[5]  Philippe Flajolet,et al.  Probabilistic Counting Algorithms for Data Base Applications , 1985, J. Comput. Syst. Sci..

[6]  Jon M. Kleinberg,et al.  Spatial gossip and resource location protocols , 2004, J. ACM.

[7]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1984, JACM.

[8]  Edith Cohen,et al.  Maintaining time-decaying stream aggregates , 2006, J. Algorithms.

[9]  John Anderson,et al.  Wireless sensor networks for habitat monitoring , 2002, WSNA '02.

[10]  Hongjun Lu,et al.  Continuously maintaining quantile summaries of the most recent N elements over a data stream , 2004, Proceedings. 20th International Conference on Data Engineering.

[11]  Jennifer Widom,et al.  Models and issues in data stream systems , 2002, PODS.

[12]  Bruce G. Lindsay,et al.  Approximate medians and other quantiles in one pass and with limited memory , 1998, SIGMOD '98.

[13]  Piotr Indyk,et al.  Stable distributions, pseudorandom generators, embeddings, and data stream computation , 2006, JACM.

[14]  Divesh Srivastava,et al.  Reverse Nearest Neighbor Aggregates Over Data Streams , 2002, VLDB.

[15]  Van Jacobson,et al.  Congestion avoidance and control , 1988, SIGCOMM '88.

[16]  Piotr Indyk,et al.  A small approximately min-wise independent family of hash functions , 1999, SODA '99.

[17]  Mahesh Viswanathan,et al.  An Approximate L1-Difference Algorithm for Massive Data Streams , 2002, SIAM J. Comput..

[18]  Piotr Indyk,et al.  Maintaining Stream Statistics over Sliding Windows , 2002, SIAM J. Comput..

[19]  Baruch Awerbuch,et al.  Randomized distributed shortest paths algorithms , 1989, STOC '89.

[20]  Luca Trevisan,et al.  Counting Distinct Elements in a Data Stream , 2002, RANDOM.

[21]  Edith Cohen,et al.  Size-Estimation Framework with Applications to Transitive Closure and Reachability , 1997, J. Comput. Syst. Sci..

[22]  Alan M. Frieze,et al.  Min-Wise Independent Permutations , 2000, J. Comput. Syst. Sci..

[23]  Rajeev Motwani,et al.  Approximate Frequency Counts over Data Streams , 2012, VLDB.

[24]  Gregory J. Pottie,et al.  Instrumenting the world with wireless sensor networks , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[25]  Leonidas J. Guibas,et al.  Randomized incremental construction of Delaunay and Voronoi diagrams , 1990, Algorithmica.

[26]  Srikanta Tirthapura,et al.  Distributed Streams Algorithms for Sliding Windows , 2002, SPAA '02.

[27]  Mike Paterson,et al.  Progress in Selection , 1996, SWAT.

[28]  Hector Garcia-Molina,et al.  Routing indices for peer-to-peer systems , 2002, Proceedings 22nd International Conference on Distributed Computing Systems.

[29]  Wei Hong,et al.  Proceedings of the 5th Symposium on Operating Systems Design and Implementation Tag: a Tiny Aggregation Service for Ad-hoc Sensor Networks , 2022 .

[30]  Jon M. Kleinberg,et al.  Spatial gossip and resource location protocols , 2001, JACM.

[31]  Deborah Estrin,et al.  Coping with irregular spatio-temporal sampling in sensor networks , 2004, CCRV.

[32]  Edith Cohen,et al.  Efficient estimation algorithms for neighborhood variance and other moments , 2004, SODA '04.

[33]  Deborah Estrin,et al.  Computing aggregates for monitoring wireless sensor networks , 2003, Proceedings of the First IEEE International Workshop on Sensor Network Protocols and Applications, 2003..

[34]  Sanjeev Khanna,et al.  Space-efficient online computation of quantile summaries , 2001, SIGMOD '01.

[35]  Mani B. Srivastava,et al.  Poster abstract: spatial average of a continuous physical process in sensor networks , 2003, SenSys '03.

[36]  Srinivasan Seshan,et al.  Cache-and-query for wide area sensor databases , 2003, SIGMOD '03.

[37]  Edith Cohen,et al.  Structure Prediction and Computation of Sparse Matrix Products , 1998, J. Comb. Optim..

[38]  QUTdN QeO,et al.  Random early detection gateways for congestion avoidance , 1993, TNET.