1. Operator Placement for In-Network Stream Query Processing U. Srivastava, K. Mungala, and J. Widom, PODS 2005 ICS280 class presentation by Iosif Lazaridis (Winter 2005)

2. Problem Motivation

3. Previous Solutions Push all data to the server: queries are processed there –Does not utilize in-network resources Push simple filters to the leaf nodes –e.g., “select all values >3” Perform aggregation in intermediate nodes But what about expensive operations? –e.g., filters over image data, or operations involving remote lookups

4. Basic System Model Let s(F) be the selectivity of a filter –i.e., the fraction of tuples it allows to pass Let c(F,i) be the per-tuple cost of a filter at level i –It is c(F,i+1)=γ j c(F,i) Let l i be the cost of network transmission of a tuple from N i to N i+1

5. Basic theorem: Rank Placing filters in order of increasing rank is optimal: rank(F) = cost(F) / (1-selectivity(F)) Intuition: –Evaluate “cheap” filters early –Evaluate very “strict” filters early

6. Problem Statement n filters and m levels of hierarchy Hence: m n possible filter placements Problem: choose optimal plan from m n different choices A greedy and an optimal algorithm

7. Greedy Algorithm Let c(P,i) be the cost of plan P incurred at node i –i.e., the cost of applying the filter and transmitting the results to i+1 –Greedy Algorithm: minimize c(P,1) by choosing a set of filters F 1 from total set F then minimize c(P,2) by choosing F 2 from F- F 1 etc. –Choose all filters with rank less than l 1

8. Example FilterSelectivityCostRank F1F1 0.81050 F2F2 0.637.5 F3F3 0.512 Then, evaluate {F 3, F 2 } in node 1 Cost = 1+0.5*3+0.5*0.6*15=7 Better than e.g., {} (cost=15) or {F 3, F 2, F 1 } (cost = 1+0.5*3+0.5*0.6*0.8*15=9.1) 12l 1 =15 Three filters: {F1, F2, F3}

9. Why Greedy is not optimal FilterSelectivityCost(1)Cost(2) F1F1 0.8108 F2F2 0.632.4 F3F3 0.510.8 Previous plan {F 3, F 2 } then {F 1 } has total cost = 7+0.5*0.6*8=9.4 Consider plan {F 3, F 2, F 1 } then {} (total cost=9.1)

10. Optimal Algorithm Model a link as a filter with selectivity γ i and cost l i Each node has an “incoming” and an “outgoing” link –Evaluate all filters with rank between the ranks of incoming and outgoing transmission“filters” If the rank of the incoming link is greater than of the outgoing link –Optimally “short-circuit” node = don’t evaluate any filters on the node

11. Processing Joins Two input streams R, S with rates r 1, r 2 Output stream consists of tuples (r,s) with r in R and s in S Join cost = ar 1 +br 2 +cr 1 r 2 –Order filters that apply on r and s separately –Order filters that apply to (r,s) Example: “temperature>10 and temperature 100 and temperature+0.5*pressure>120” Join Rate r 1 Rate r 2 Filters F 1 Filters F 2 temperature>10 pressure>100 temperature<20 Filters F 1,2 temperature+0.5*pressure>120

12. Conclusions Systematic way to push filters into the network, taking into account their relative cost and the capabilities of nodes Perhaps does not take into account practical issues such as broadcast communication or faults Interesting to see practical values for γ, c, s in a real deployment.