RandPing: A Randomized Algorithm for IP Mapping

1. RandPing: A Randomized Algorithm for IP Mapping Michelle Liu Yuhan Cai

2. Outline • Introduction • Related Work • Background • Algorithm Overview • Experimental Evaluation • Conclusions and Future Work

3. Introduction • Motivations • Collection of personalized information • Authorities of transactions • Problem statement • IP mapping is the problem that, given an IP address p, find the geographic location of the internet host with IP address p. • Challenges • No authorative database • IP addresses do not contain geographic information

4. Related Work • DNS based approach • Using DNS records from databases • IP2LL, NetGeo, and GeoTrack • DNS might not be related to locations • Delay based approach • Exploiting relationship between distances and network delays • GeoPing and CBG • Clustering based approach • Splitting IP address space into clusters • Assumption: all hosts within the same cluster are co-located

5. Background • Best line bound • Above the baseline • Below all data points • Closest to all data points

6. Background (cont.) • Clustering • Partitioning Around Medoids (PAM) • Quality of a Clustering = average of the distance of an object to the medoid of its cluster • Outlier detection • O is a DB(p, D)-outlier if at least fraction p of T lies greater than distance D from O. • Scriptroute system • A system that allows network measurements conduction from remote vantage points

7. Algorithm Overview • Overall idea • Clustering probing machines • Random selection of a small set of probing machines • Reduction of search space by pruning • Major steps • Preprocessing stage • Randomized pinging • Location estimation

8. Preprocessing Stage • Construction of RTT table and Distance table for probing machines • Computation of the best line for each probing machine subject to the constraint:

9. Preprocessing (cont.) • Clustering of probing machines based on their geographic locations • Transformation of the geographic system to a Cartesian coordinate system • x = 2RcosT0 (G – G0) / 360 • y = 2R (T - T0) / 360

10. Randomized Pinging • Random selection of m clusters • Random selection of k probing machines within each cluster • Pinging the target machine to get n = m*k RTT measurements

11. Location Estimation • Computation of estimated distances • Determination of the best group of circles by dynamic programming • Keep track of groups of circles • Incrementally build up each group • Pick the biggest group

12. Location Estimation (cont.) • Locating the target machine by non-linear programming subject to the constraints:

13. Location Estimation (cont.) • Repeat the process for r times • Computation of the centroid for the r estimated locations • Prune out distance-based outliers • Compute the centroid of the points left

14. Experimental Results • Setup • Machines selected from Planetlab in US • One small set of machines to be target machines, the rest to be probing machines • Results • Error distance: distance between the real location of the target machine and the estimated one

15. Experimental Results (cont.)

16. Experimental Results (cont.)

17. Experimental Analysis • Limited number of probing machines • Effect of randomization is not obvious • The best line estimation is too conservative. • Intersection region of the circles is too big.

18. Conclusions • A randomized approach for IP mapping using clustering and outlier detection • Location estimation based on dynamic programming and non-linear programming

19. Future Work • Adjusting the algorithm parameters: • number of clusters • number of trials and • number of picked machines • Proving a lower bound for the difference between the accuracy of randomized algorithm and deterministic algorithm