1. Boston University Computer Science On The Marginal Utility of Network Topology Measurements John Byers with Paul Barford (now at Wisconsin), Azer Bestavros, and Mark Crovella

2. Measurement Philosophy zCurrent Dogma: When conducting a wide-area measurement study: “more is better.” yMore = measurements yMore = measurement sites zTrue, but taking more measurements and deploying more infrastructure is expensive! zOur focus: How much better is more? yEven harder: When can we stop measuring? zNot much work on this topic in our community.

3. Problem Instance: Discovering Internet Topology zTypical goal: discover the router-level Internet graph zTypical approach: merge lists of known nodes and edges zTraceroute reports the IP path from A to B yi.e., how IP paths are overlaid on the router graph

4. Traceroute studies zYield overlays of projections from S’s to D’s ySources: active, expensive yDestinations: passive, cheap S S D D D D D

5. Motivating Questions zHow should we use traceroute and what can it discover? yPhysical topology (nodes, links)? yIP routing topology? zWhat’s a good way to organize a collection-of- traceroutes study? yMany sources? yMany destinations? yHow much is enough?

6. Theoretical Inroads zTake a graph G = (V, E) and a routing algorithm R. zChoose j sources and k destinations at random. zConsider the subgraph G’ = (V’, E’) induced by routes from R between all (S, D) pairs. zHow do expected values of |V’| and |E’| scale as a function of j and k ? zChuang-Sirbu scaling law is special case for j = 1. zMarginal utility of adding k+1 ’st source or destination is expected contribution to |V’| or |E’|.

7. What might we expect? zTwo extremal cases: yClique: each new (S, D) discovers a new path yStar: each new S or D discovers only a small neighborhood D D D D D D D D D D S S S S Clique Star

8. Skitter to the Rescue zTwo datasets from CAIDA zSmall dataset: May 2000 y8 sources, 1277 destinations, 20K paths ySources in: New Zealand, Japan, Singapore, San Jose (2), Ottawa, London, Washington yAll sources traced to all destinations zLarge dataset: October 2000, 30 times bigger y12 sources, 313709 destinations, 600K paths yNo destination common to all sources, or vice versa

9. Interface Disambiguation zTraceroutes report only on interfaces used yRouters often have multiple interfaces yBut merging traceroutes requires matching routers zSolution: probe each interface from some site X yRouters are supposed to respond on the interface used for routing to X zResults in set of (probe interface, response interface) pairs yEach connected component is taken to be a router

10. Classifying Nodes zCore, border, stub, leaf zSolely from traceroute information LeafBorderCoreStub

11. Classification depends on msmts Core Stub Border

12. Limitations and Caveats zInterface disambiguation y13% of interfaces never responded zNode classification yIdentifying a border node requires two paths to it zRepresentativeness yDatasets are small, may not be representative ySkitter sources not selected at random zUnknown coverage of true network yDiminishing returns may not signify good coverage

13. Diminishing Returns (Small Dataset)

14. Diminishing Returns (Large Dataset)

15. Diminishing returns by Classification (Small Dataset) Core Stub Border

16. What Does This Suggest? D D D D D D S S

17. Adding Destinations: Nodes Slope is about 3

18. Adding Destinations: Links Slope is about 4

19. Add Sources or Destinations? Isolines represent constant node discovery, varying S’s or D’s

20. Node Degree Distribution 8 Sources 1 Source

21. Node Degree Distribution: Tail 1 Source 8 Sources

22. Degree distribution convergence: RMSE

23. Information Theory Plug Link Discovery zCan compare marginal utility of different processes. Node Discovery

24. Related Work zPansiot & Grad ’98 yFirst multi-traceroute study ySimilar methodology, incl. interface disambiguation zChuang & Sirbu ’98 Phillips, Shenker & Tangmunarunkit ’99 ysingle-source case, found sublinear growth of multicast tree with added destinations zGovindan & Tangmunarunkit ’00 yExtensive node discovery, overcoming limitations of traceroute zBroido & Claffy ’01 yLarger datasets; more detailed look at graph structure

25. Conclusions zRigorous quantification of marginal utility of additional measurements. zTo discover all physical nodes, traceroute is inefficient yDiminishing returns: many S’s and D’s needed zTrading off S’s and D’s yAdding destinations seems more cost-effective zTo discover how “typical” routes pass through network, traceroute is informative yRouting core and feeders yMuch of routing core is visible from few S’s (given enough D’s)