Partitioning the Internet

Transcription

1 Partitioning the Internet Matthias Wachs Christian Grothoff 1 Ramakrishna Thurimella 2 Technische Universität München 1 University of Denver 2 CRiSIS 2012, Cork, Ireland FSNSG (TUM) Partitioning the Internet 1

2 Motivation We think Internet is resilient and well-connected, but... FSNSG (TUM) Partitioning the Internet 2

3 Motivation How resilient is the Internet against failure of providers or links? Can the Internet be partitioned easily? How big are separator sets? FSNSG (TUM) Partitioning the Internet 3

4 Internet Backbone Autonomous Systems BGP ? AS AS AS 111 AS 141 AS 79 BGP routing table in AS 34: /24: Next Hop: , FSNSG (TUM) Partitioning the Internet 4

5 Approach Analyze Internet backbone topology: Logical AS graph Generate AS graph: AS Node Relation Edge ASes have different importance: Generate weights for ASes Use heuristic to find separators FSNSG (TUM) Partitioning the Internet 5

6 Graph Generation - BGP Routing Tables Routing tables from BGP routers: Contain AS Path RouteViews BGP Dumps Size does not matter Prefixes Nodes Edges LINX (UK) 8,414,813 35,872 75,170 SYDNEY (AU) 1,543,223 36,543 67,485 WIDE (JP) 680,980 36,315 52,885 Merged 36,697 79,464 FSNSG (TUM) Partitioning the Internet 6

7 Graph Generation - Path Measurements Forward Path Measurements: Have to be mapped to AS CAIDA IPv4 Routed /24 AS Links Dataset Nodes Edges Cycle ,416 44,371 Cycle ,376 43,654 Cycle ,343 42,273 Merged 22,271 57,867 Merged BGP and Forward Path Graphs: Nodes Edges BGP 36,697 79,464 Path Measurements 22,271 57,867 Merged 36,715 99,852 FSNSG (TUM) Partitioning the Internet 7

8 Weight Generation ASes hosting important services are more important Top 100k websites from Alexa Global DNS lookup Mapping IP to AS Number of pageviews Minimum weight FSNSG (TUM) Partitioning the Internet 8

9 Weight Generation 1e Node Weight e Autonomous Systems FSNSG (TUM) Partitioning the Internet 9

10 Background Weighted Graph: n Nodes with weight w Edges Total Weight W Separator: Set of nodes or edges partitioning the graph χ-separator (χ [ 1 2, 1)): Nodes in remaining component have weight w i < χ W 1 χ W = W = 10 χ = 0.5 W = 10 χ = 0.9 χ W = FSNSG (TUM) Partitioning the Internet 10

11 Calculating Separators Fix χ, minimize size of separator State of the Art: Metis (Karypis & Kumar) 1 Insufficient results: no good cuts for large χ large separators for weighted graphs Develop own heuristic 1 FSNSG (TUM) Partitioning the Internet 11

12 Our heuristic Based on Kernighan-Lin heuristic 3 variations: graph coarsening feasible operations move operation Simulated annealing Edges separators weighted edge separators node separators FSNSG (TUM) Partitioning the Internet 12

13 Edge Separators for Unweighted Graphs Breadth first traversal: Initial partitions A, B Minimize separator size S(A, B) Successive vertex swaps between partitions χ > 0.5 : isolated dummy nodes A B FSNSG (TUM) Partitioning the Internet 13

14 Edge Separators for Weighted Graphs Graph coarsening swap (a,b) move (a), move (b) Only feasible operations Threshold: W A, W B < χ W Apply operation with highest gain FSNSG (TUM) Partitioning the Internet 14

15 Node Separators Convert edge to node separator 1 A 4 B A 1 4 B FSNSG (TUM) Partitioning the Internet 15

16 Node Separators Minimize separator size C Simulated annealing Push(C, heat), Pull(C, heat) Push / Pull Operation: For all nodes in separator Calculate gain of feasible operation Heat: propability operation is applied FSNSG (TUM) Partitioning the Internet 16

17 Node Separators 1 A 4 B A Push 7 10 B FSNSG (TUM) Partitioning the Internet 17

18 Node Separators 1 A B A Pull 11 B FSNSG (TUM) Partitioning the Internet 18

19 Simulated Annealing Starting with infinite heat: destroy cut properties Outer Loop: Low high temperature Inner Loop: Cool down Apply push and pull operations Lower-cost moves prefered with higher probability FSNSG (TUM) Partitioning the Internet 19

20 Results Unweighted Graph Size of the edge separators for different values of χ Edge separator size Presented heuristic Metis χ FSNSG (TUM) Partitioning the Internet 20

21 Results Unweighted Graph Size of the node separators for different values of χ Node separator size Presented heuristic Metis χ FSNSG (TUM) Partitioning the Internet 21

22 Results Weighted Graph Size of the edge separators for different values of χ Edge separator size Presented heuristic Metis χ FSNSG (TUM) Partitioning the Internet 22

23 Results Weighted Graph Size of the node separators for different values of χ Node separator size Presented heuristic Metis χ FSNSG (TUM) Partitioning the Internet 23

24 Discussion Internet is hard to partition: Failure of ASes to make 40% of HTTP request fail New heuristic to find node end edge separators: Capable of large problem size Elements of Separator: critical infrastructure useful for traffic monitoring economic decisions FSNSG (TUM) Partitioning the Internet 24

25 Discussion Issues: Internet Exchange Points (IXPs) Undersea cables Improve Logical Graph: Improved Measurement Physical Map Geographical Map FSNSG (TUM) Partitioning the Internet 25

26 End Thank you! Data and source available on: FSNSG (TUM) Partitioning the Internet 26

27 Weight Generation - Detail Top 100k websites 89 Planetlab nodes 3 iterations (load balancing, caching) IP adresses: 27,801,818 Lookups failed: 1,269,239 Invalid IPs: 18,066 Unique IPs: 159,247 FSNSG (TUM) Partitioning the Internet 27

28 Graph Generation - BGP /24: Next Hop: , Nodes: 776, 79, 111 Edges: , AS Sets: MOAS: Due to route aggregation Not added Same prefix announced from multiple ASes ASes were merged Add edge for every AS IXPs: Represented as strongly connected nodes Important links: Multiple logical links FSNSG (TUM) Partitioning the Internet 28

29 Graph Generation - Traceroute Traceroute from to : * * * Mapping to AS AS AS AS 776 * * * AS 111 Nodes: 34, 776, 111 Edges: FSNSG (TUM) Partitioning the Internet 29