Characterizing and Exploiting Reference Locality in Data Stream Applications Feifei Li, Ching Chang, George Kollios, Azer Bestavros Computer Science Department Boston University

Data Stream Management System Application Result Query (e.g. Joins over two streams) Unselected tuples Query Processor Select tuples that maximize the query metrics Memory Data Stream Management System (DSMS)

Observations Storage / Computation limitation Full contents of tuples of interest cannot be stored in memory. Cast as “caching” problems Query processing with memory constraint.

“Caching” Problem in DSMS sliding window joins window size sum of is the memory size What tuples to store to max the size of join results? Locality of reference properties (Denning & Schwatz)

Locality-Aware Algorithms Our Locality-aware algorithms Previous algorithms

Our Contributions Cast query processing with memory constraint in DSMS as “caching” problem and analyze the two causes of reference locality Provide a mathematical model and simple method to infer it to characterize the reference locality in data streams Show how to improve performance of data stream applications with locality-aware algorithms

Reference Locality - Definition In a data stream recently appearing tuples have a high probability of appearing in the near future.

Inter Arrival Distance (IAD) A random variable that corresponds to the number of tuples separating consecutive appearances of the same tuple. 2 4 10 7 … 3 1 IAD

Calculate distribution of IAD … i a b e c a i … xn xn+k distance is k Where pi is the frequency of value i in this data stream

Sources of Reference Locality Long-term popularity vs. Short-term correlation (web traces, Bestavros and Crovella) MS IBM GG Reference locality due to long-term popularity … For example: Stock Traces A MS GG IBM Reference locality due to short-term correlation … George’s Company A listed today!

Independent Reference Model With the independent, identically-distributed (IID) assumption: Problem: only captures reference locality due to skewed popularity profile.

Metrics of Reference Locality How to distinguish the two causes of reference locality? … A MS A A MS GG GG MS IBM … Original Data Stream S MS A GG IBM Random Permutation of S … Compare IAD distribution of the two!

Stock Transaction Traces Daily stock transaction data from INET ATS, Inc. Zipf-like Popularity Profile (log-log scale)

Stock Transaction Traces Still has strong reference locality, due to skewed popularity distribution CDF of IAD for Original and Randomly Permuted Traces

Network OD Flow Traces Network traces of Origin-Destination (OD) flows in two major networks: US Abilene and Sprint-Europe Zipf-like Popularity Profile (log-log scale)

Network OD Flow Traces CDF of IAD for Original and Randomly Permuted Traces

Outline Motivation Reference Locality: source and metrics A Locality-Aware Data Stream Model Application of Locality-Aware Model Max-subset Join Approximate count estimation Data summarization Performance Study Conclusion

Locality-Aware Stream Model Recent h tuples … 2 2 4 10 5 10 7 7 5 xn Index xn-h P(xn=xn-4)=a4 xn-1 Popularity Distribution of S P Recent h tuples of S stream S

Locality-Aware Stream Model Recent h tuples … 2 2 4 10 5 10 7 7 2 xn P(xn=2 from popularity profile)=b*p(2) Index xn-h xn-1 Popularity Distribution of S P Recent h tuples of S stream S

Locality-Aware Stream Model Xn= Xn-i with probability ai Y with probability b where 1  i  h, and Y is a IID random variable w.r.t P, and where (xk,c)=1 if xk=c, and 0 otherwise. Similar model appears for caching of web-traces, example Konstantinos Psounis, et. al

Make N observations, infer ai and b (h+1) parameters Infer the Model Expected value for xn: Least square method: minimize over a1, … , ah, b: Make N observations, infer ai and b (h+1) parameters

Model on Real Traces- Stock b: degree of reference locality due to long-term popularity 1-b: … due to short-term correlation

Model on Real Traces- OD Flow

Utilizing Model for Prediction S … xn-h … xn-1 xn xn+1 xn+2 … xn+T … T The expected number of occurrence for tuple with value e in a future period of T, ET(e). Using only T+1 constants calculated based on the locality model of S

Outline Motivation Reference Locality: source and metrics A Locality-Aware Data Stream Model Application of Locality-Aware Model Max-subset Join Approximate count estimation Data summarization Performance Study Conclusion

Approximate Sliding Window Join sliding window joins window size sum of is the memory size What tuples to store to max the size of join results?

Existing Approach Metrics: Max-subset Previous approach: Random load shedding: poor performance (J. Kang et. al, A. Das et. al) Frequency model: IID assumption (A. Das et. al) Age-based model: too strict assumption (U. Srivastava et. al) Stochastic model: not universal (J. Xie et. al)

Marginal Utility 6 5 10 8 12 … Stream S Stream R n n-1 T=5

Calculate Marginal Utility S … 10 x 13 x 8 x x 8 9 … n Tuple Index: x ? P1 x ? P2 … R … 9 7 n Based on locality model, we can show that: where F depends the characteristic equation of Pi which is a linear recursive sequence!

ELBA Exact Locality-Based Algorithm (ELBA) Based on the previous analysis, calculate the marginal utility of tuples in the buffer, evict the victim with the smallest value Expensive

LBA Locality-Based Algorithm (LBA) Assume T is fixed, approximate marginal utility based on the prediction power of locality model. Depends on only T+1 constants that could be pre-computed.

Space Complexity A histogram stores both P over a domain size D and T+1 constants histogram space usage is poly logarithm: O(poly[logN]) space usage for N values (A. Gilbert, et. al)

Sliding window join: varying buffer size – OD Flow

Sliding window join: varying buffer size - Stock

Sliding window join: varying window size - stock

Conclusion Reference locality property is important for query processing with memory constraint in data stream applications. Most real data streams have strong temporal locality, i.e. short term correlations. How about spatial locality, i.e. correlation among different attributes of the tuple?

Thanks!

Approximate Count Estimation Derive much tighter space bound for Lossy-counting algorithm (G. Manku et. al) using locality-aware techniques. Tight space bound is important, as it tells us how much memory space to allocate.

Data Summarization Define Entropy over a window in data stream using locality-aware techniques, instead of the normal way of entropy definition. Important for data summarization, change detection, etc. For example: 1 2 3 …

Data Stream Entropy Data Streams Locality-Aware Entropy Uniform IID 6.19 Permuted Stock Stream 5.48 Original Stock Stream 3.32 Higher degree of reference locality infers less entropy