1. IDMaps: A Global Internet Host Distance Estimation Service P. Francis, S. Jamin, C. Jin, Y. Jin, D. Raz, Y. Shavitt, L. Zhang Presenter: Zhenying Liu

2. Contents Background Goals Related work Architecture Performance Evaluation Conclusion

3. Background Increasing need to learn network distances, bandwidth One method Measure the distance by itself(ping, traceroute) A useful general service: quick, efficient SONAR, Feb. 1996 HOPS(Host proximity Service) Need underlying measurement infrastructure to provide distance measurements

4. Contents Background Goals Related work Architecture Performance Evaluation Conclusion

5. IDMaps Internet Distance Map Service To be underlying service that provides the distance information used by SONAR/HOPS Goals Not near instantaneous information Determine roughly the best service given technology constraints Consider whether there are applications for which this level of service would be useful

6. Resulting Goals Separation of functions Separation of IDMaps and the query/reply service Distance Metrics Latency(round-trip delay) useful, easy to provide Bandwidth Useful, difficult to provide, expensive to measure Accuracy of the distance information High accuracy: difficult to achieve To obtain accuracy within a factor of 2

7. Contents Background Goals Related work Architecture Performance Evaluation Conclusion

8. Alternative Architectures and Related Work SPAND, Remos: provide only distance information between hosts close to a distance server and remote hosts on the internet For each server: scales proportionally to the number of destination For all sites in the Internet: N 2 Stemm: passive monitoring Not perturb actual internet traffic Only measure regions previous traversed Not adapt to the internet topology changes More human efforts

9. Contents Background Goals Related work Architecture Performance Evaluation Conclusion

10. IDMaps Architecture Address three questions What form does the distance information take? What are IDMaps’ components? How should the distance information be disseminated?

11. Various forms of distance information FormsScalecomments Global IP addr.H 2 H: # of hosts Infeasible Addr. Prefix(AP)P 2 P: # of APs; 200,000 Easily terabytes ASA 2 +P’ ( A<<P ) A: # of AS, P’:# of BGP-advertised IP addr. Blocks A = 100,000 (large) Its accuracy is highly suspected Cluster of APsB 2 +P B: # of Traces If B = 500, manageable Reasonable accuracy 1 2 3 4

12. 1 2 3 4

13. The form used There are three main components APs, Tracers, and the virtual links(the raw distance) AP: a consecutive address range of IP addresses Tracers: Some systems that are distributed around the Internet Assumption We can estimate the distance between two points as the sum of distances between intermediate points

14. AP1 AP2 Tracer1 b a c |a-c|<|b|<|a+c| ? Feasible to estimate distance? -- APs -- Tracers An assumption: Triangulation

15. To support the triangulation Set up 2 experiments: D1(1995), D2(1997) Fig. Shows the ratios of for all shortest-path triangulation in the data sets Between 75% an 90% of triangulation estimates fall within a factor of 2 of the real distance The resulting estimates are acceptable!

16. Tracer placement Two problems How many tracers are optimal? Given the number of tracers, how to put to minimize the maximum distance between an AP and the nearest tracer? Two graph theoretic approaches that can apply K-HST algorithm Minimum K-center algorithm These algorithms are used to determine the placement of fire stations, ambulance placement, etc. with a priori

17. k-HST: decide # of tracers 1 st phase: The graph is recursively partitioned: A node is arbitrarily selected from the current(parent) partition, and all the nodes that are within a random radius from this node form a new node partition The radius of the child partition is a factor of k smaller than the diameter of the parent partition Recurs until each node is in a partition of its own

18. k-HST tree 2 nd phase: virtual node is assigned to each of the partition on each level The diameter of a partition The furthest distance between two nodes in the partition Equals to 2 times of the length of the links from a virtual node to its children

19. Use K-HST tree Devise a greedy algorithm to find the number of tracers when the maximum distance is bounded to D Push the tracers down the tree until it discovers a partition with diameter <=D The number of partitions is the minimum number of tracers Set the virtual nodes of these partitions to be the tracer

20. Minimum K-Center Algorithm K-Center problem The placement of a given number of centers such that the maximum distance from a node to the nearest center is minimized NP-complete Willing to tolerate inaccuracies within a factor of 2(2-approximation) No worse than twice the maximum Observation: Guarantee that the distance from a node to the nearest center is bounded

21. Minimum K-Center Algorithm: details G=(V,E), E=V×V, c(e) is the cost of the shortest path between (v 1, v 2 ) All the graph edges are arranged in non-decreasing order by cost G i 2 is the graph whenever there is a path between u and v in G i of at most two hops, u  v An independent set of a graph G(V,E) is such that, for all u,v  V’, the edge (u,v) is not in E An independent set of G i 2 is thus a set of nodes in G i that are at least 3 hops apart in G i The maximal independent set M as an independent set V’ such that all nodes in V-V’ are at most one hop away from nodes in V’

22. 1. Construct G i 2,G 2 2,…, G m 2 2. Compute Mi for each G i 2 3. Find the smallest I such that |M i |<=K, say j 4. M j is the set of K centers Algorithm 2 (2-approximate minimum-center [18]): details

23. Tracer Heuristics Stub-AS only connected to one other AS Transit-AS connected to one or more other AS allows itself to be used as a conduit for traffic (transit traffic) between other AS's Most large ISPs are Transit-AS’s Mixed Randomly, with uniform distribution placed on the network

24. Virtual links Tracer-tracer virtual links Not necessary to list all B 2 tracer-tracer distances Given a number of tracers in Seattle and Boston It would almost certainly not to be useful to know all of the distance between them Allow a sufficient distance approximation between hosts in Seattle and hosts in Boston

25. Virtual links Tracer-AP VLs A dedicated tracer? More than one tracer? C in AP1 will be directed to mirror M1 in AP3 instead of M2 in AP2 Had tracer T2 also traced to AP1, the client would have been directed to M2

26. Contents Background Goals Related work Architecture Performance Evaluation Conclusion

27. Performance Evaluation Topology Generation Waxman, Tiers, Inet Simulating IDMaps Infrastructure Tracer placement: Stub-AS, Transit-AS Distance map computation Tracer-tracer VLs and Tracer-AP VLs

28. Performance Metric Computation Nearest mirror selection P app : the percentage of correct IDMaps’ answers over total number of clients Consider IDMaps’ server selection correct As long as the distance between a client and the nearest mirror determined by IDMaps is within a factor of λ times the distance between the client and the actual nearest mirror ( we use λ=2)

29. Simulation result Mirror selection using IDMaps gives noticeable improvement over random selection Network topology can affect IDMaps’ performance Tracer placement heuristics that do not rely on network topology can perform as well or better than algorithms that requires a priori knowledge of the topology

30. Simulation result Adding more tracers gives diminishing return Number of tracer-tracer VLs required for good performance can be on the order of B with a small constant Increasing the number of tracers tracing to each AP improves IDMaps’ performance with diminishing return

31. Mirror selection Transit-AS The probability of that at least 80% of all clients will be directed to the “correct” mirror is 100% Up to 98% of all clients will be directed to the correct mirror is only 85%

32. Mirror selection Mirror selection using distance maps outperforms random selection regardless of the tracer placement algorithm Qualitatively, the results from agree with the conclusion: mirror selection using distance maps outperforms random selection

33. Effect of Topology

34. Performance on Tiers generated topology exhibit a qualitatively different behavior than those on other topologies The transit-AS heuristic gives better IDMaps performance than the k-HST algorithm on topologies generated from Inet and Waxman, but not so in the topologies generated from Tiers

35. Contents Background Goals Related work Architecture Performance Evaluation Conclusion

36. A global distance measurement infrastructure called IDMaps is purposed It can be placed on the Internet to collect distance information Nearest mirror selection fro clients Significant improvement over random selection Do not require a full knowledge of the underling topology

37. Conclusion IDMaps overhead can be minimized by grouping Internet addresses into APs to reduce the number of measurements Apply t-spanner to tracer-tracer VLs can result in linear measurement overhead with respect to the number of tracers in the common case Overall, this study has provided positive results to demonstrate that a useful Internet distance map service can indeed be built scalably

38. (Stub AS)