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1 Incentive-Compatible Interdomain Routing Joan Feigenbaum Yale University Vijay Ramachandran Stevens Institute of Technology Michael Schapira The Hebrew University

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2 Interdomain Routing Establish routes between autonomous systems (ASes). Currently done with the Border Gateway Protocol (BGP). AT&T Qwest Comcast Verizon

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3 Why is Interdomain Routing Hard? Route choices are based on local policies. Autonomy: Policies are uncoordinated. Expressiveness: Policies are complex. AT&T Qwest Comcast Verizon My link to UUNET is for backup purposes only. Load-balance my outgoing traffic. Always choose shortest paths. Avoid routes through AT&T if at all possible.

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4 Welfare-Maximizing Routing AS 1 AS n Mechanism p1p1 pnpn v n (. ) v 1 (. ) a1a1 anan Private information: Route valuations Strategies For each destination (independently / in parallel), compute: A confluent routing tree that maximizes the sum of nodes’ valuations for that destination, i.e., ∑ i v i (R i ) ; and VCG payments (nodes are paid for their contribution to the routing tree) … using a BGP-compatible (distributed) algorithm. Routes R 1, …, R n

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5 VCG Payments The VCG payment to node k is of the form p k = ∑ i k v i (T d ) – h k () where h k is a function that does not depend on k’s valuation. If h k ({v i }) = ∑ i ≠ k v i (T d -k ), then the payment to each node is p k (T d ) = ∑ i ≠ k [v i (T d ) – v i (T d -k )]. T d is the optimal routing tree to destination d. T d -k is the optimal tree to d if node k is removed.

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6 Payment Components The total payment to node k can be broken down into payment components: p k (T d ) = ∑ i ≠ k p k i (T d ). Each payment component depends only on the valuations at some node i: p k i (T d ) = v i (T d ) – v i (T d -k ). Compute these in a distributed manner. Problem: We don’t want to run an algorithm for every T d -k (not efficient).

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7 Routing-Protocol Desiderata Does not assume a priori knowledge of the network topology Distributed Autonomy-preserving Dynamic (responds to network changes) Space- and communication-efficient Complies with Internet next-hop forwarding

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8 BGP Route Processing The computation of a single node repeats the following: Receive routes from neighbors Update Routing Table Choose “Best” Route Send updates to neighbors Paths go through neighbors’ choices, which enforces consistency. Decisions are made locally, which preserves autonomy. Uncoordinated policies can induce protocol oscillations. (Much recent work addresses BGP convergence.) Recently, private information, optimization, and incentive-compatibility have also been studied.

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9 Known Results: Welfare Maximization and Interdomain Routing Routing-Policy Class Good Centralized Algorithm? Good Distributed Algorithm? LCP* General Policy (and hard to approximate) Next Hop Subjective Cost (incl. some special cases) (approx. is easy if >1 tree) Forbidden Set

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10 Question These are mostly negative results. Is there a realistic and useful class of routing policies (i.e., something broader than LCPs) for which we can get an incentive-compatible, BGP-compatible algorithm to compute routes and payments?

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11 Gao-Rexford Framework (1) Neighboring pairs of ASes have one of: –a customer-provider relationship (One node is purchasing connectivity from the other node.) –a peering relationship (Nodes have offered to carry each other’s transit traffic, often to shortcut a longer route.) peer providers customers peer

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12 Gao-Rexford Framework (2) Global constraint: no customer-provider cycles Local preference and scoping constraints, which are consistent with Internet economics: Gao-Rexford conditions => BGP always converges [GR01] Preference Constraints... i d R1R1 R2R2 k2k2 k1k1 If k 1 and k 2 are both customers, peers, or providers of i, then either ik 1 R 1 or ik 2 R 2 can be more valued at i. If one is a customer, prefer the route through it. If not, prefer the peer route. Scoping Constraints d k i j Export customer routes to all neighbors and export all routes to customers. Export peer and provider routes to all customers only. m.. peer customer provider

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13 Efficient Payment Computation Next-hop valuations: The valuation of a route depends only on its next hop. Theorem: If Gao-Rexford conditions hold and ASes have next-hop policies, then routes and payments can be computed with “good” space efficiency. *(We only run “BGP” once.)

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14 Next-Hop Payment Computation Send augmented BGP update message whenever best route or availability of a k-avoiding route changes: When an update message is received: –Store path and bits in routing table. –Scan bits to update best k-avoiding next hop. AS k 1 AS k 2 …AS k i Y/N … AS Path k i -avoiding path known?

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15 Next-Hop Routing Table Store usable routes, availability of k-avoiding routes from neighbors (for all stored routes), and best k-avoiding next hops (for current most preferred route). Payment components are derived from next hops: p k i (T d ) = v i (T d ) – v i (T d -k ) for transit k ; = 0 otherwise. Destination d AS 2 AS 4AS 5 Optimal AS path Y Y Bit vector from update AS 1 AS 2 Best k-avoiding next hops d AS 1 AS 3AS 5 Alternate AS path Y Y Bit vector from update

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16 Towards a General Theory Gao-Rexford + Next-Hop valuations are a special case. We identify a broad sufficient condition for valuations that permit BGP-compatible, incentive-compatible computation of routes and VCG payments.

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17 Dispute Cycles Relation 1: Subpath... R1R1 R2R2 R 1 R 2 Relation 2: Preference... Q1Q1 Q2Q2 v i (Q 1 ) > v i (Q 2 ) Q 1 Q 2 d d i i Valuations do not induce a dispute cycle iff there is no cycle formed by the above relations on all permitted paths in the network. No dispute cycle => robust BGP convergence [GSW02, GJR03]

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18 Example of a Dispute Cycle 1 2 d 3 v(12d) = 10 v(1d) = 5 v(23d) = 10 v(2d) = 5 v(31d) = 10 v(3d) = 5 1d1d2d2d3d3d 31d12d23d Dispute Cycle Subpath Preference

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19 Policy Consistency..... d k i IF v k (R 1 ) > v k (R 2 ) R2R2 R1R1 THEN v i ((i,k)R 1 ) > v i ((i,k)R 2 ) Valuations are policy consistent iff, for all routes R 1 and R 2 (whose extensions are not rejected), (analogous to isotonicity [Sob.03])

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20 Optimality Theorem: If the valuation functions are policy consistent and do not induce a dispute cycle, then BGP converges to the globally optimal routing tree.

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21 Efficiently Computing Payments Local optimality: In a globally optimal routing tree, every node gets its most valued route. Theorem A: No dispute cycle + policy consistency => local optimality. Theorem B: Local optimality => If k is not on the path from i to d, then payment component p k i (T d ) = 0.

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22 Conclusions Gao-Rexford + Next-Hop valuations are a reasonable class of policies that admit incentive-compatible, BGP-compatible computation of routes and VCG payments. Only a constant-factor increase in BGP routing-table size is required. Dispute-cycle-free and policy-consistent valuations generalize this result.

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23 Future Work Approximability of the interdomain-routing problem? –Without restrictions on policies, no good approximation ratio is achievable [FSS04]. Remove bank? Optimal communication complexity?

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24 Technical Report Full version of this paper is available as Yale University Technical Report YALEU/DCS/TR-1342 http://www.cs.yale.edu/publications/ techreports/tr1342.pdf

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