1. Planning the Transformation of Network Topologies Young Yoon 1, Nathan Robinson 2, Vinod Muthusamy 3, Sheila McIlraith 2, Hans-Arno Jacobsen 2 1 Samsung Electronics, 2 University of Toronto, 3 IBM T.J. Watson Research Center

2. The Need for Transforming a Topology 15 2 4 0 63 15 2 4 0 63 Old topology New topology Message stream P1P1 S1S1 S1S1 P1P1 S2S2 P2P2 S2S2 P2P2 Removable edge Goal edge 2 Minimize the number of nodes Optimizing path lengths or message latencies Controlling node degrees Provisioning sufficient network capacity Topology Optimization Criteria Google Pub/Sub (GooPS): Reconfigurable messaging substrate for their public services Yahoo! PNUTS Large-scale data dissemination overlay network Openflow : Supports rewiring virtual topologies Real World Problems

3. Transform “incrementally” using primitive transformation operators k ji k ji Initial state Goal state SHIFT(i, j, k) r g Theorem: Can transform any acyclic connected graph to any other acyclic connected graph Keeps the integrity of message delivery during the transformation No message loss No message reordering No transient loops 3

4. Many Ways to Transform Incrementally 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 Start S1S1 S2S2 S3S3 S4S4 S5S5 S6S6 S7S7 Goal Removable edge Goal edge 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 15 2 4 0 63 Start S1S1 S2S2 S3S3 Goal 4

5. Incremental Topology Transformation (ITT) as an Automated Planning Problem Network topology is a connected UAG T = (V, E): – V is a set of vertices – E is a set of edges – ex (v i, v j ) ∈ E, where v i and v j ∈ V T = – T S is the initial topology – T G is the goal topology – O is a set of transformation operations Removable edge: e in a topology T S and not in T G Plan: A sequence of transformation operations that achieves T G from T S with the least cost 5

6. The Key Domain Knowledge: End-to-End Path of a Goal Edge 15 42 3 r3r3 r2r2 r1r1 Shift the removable edge on the end-to-end path between the nodes that constitute the goal edge. g 6

7. Breaking into Sub-Problems to Assess Disruption to Message Flows 15 2 4 0 63 7 Start Topology 15 26 1 2 4 0 3 15 2 4 0 63 Goal Topology Sub-problem 1 Sub-problem 2

8. The Effect of Sub-problem Solving Ordering 8 15 2 4 0 63 15 2 4 0 63 Incurs 11 routing state updates Sub-problem 1  Sub-problem 2 15 2 4 0 63 15 2 4 0 63 Incurs 5 routing state updates Sub-problem 2  Sub-problem 1

9. New Planner: Combined Pair goal and removable edges (to find the trajectory) Randomly generate k trajectory orderings Select an ordering by routing state updates For each trajectory, shift removable edge incrementally – If a shift action breaks the end-to-end path of other goal edges, Find another end-to-end path for those goal edges Re-compute the goal and removable edge pairing 9

10. New Planner: Best First Search Keep an open list (OL) of states to explore Expand the state with the least estimated cost – Heuristics: Distance from removable edge to goal edges in terms of shift movements Uses restarts to promote exploration – Expand the next best state of OL, if the state exploration limit is reached 10

11. Key Evaluation Results Parallel experiment execution on two Intel Xeon quad-core 3 GHz Randomly generated test problems: Nodes: 20-400, Degree of change: 10%-60%, Maximum degree: 5, Maximum diameter: 15, Varying distributions of node degrees 11 # of Plan Actions vs. Network SizeSolution Time vs. Network Size Set-up LAMA and PROBE 30 nodes 10% change: 8 actions in 3.64s ~18.33s > 50 nodes 50% change: Failed to fined a plan New planning system 400-node overlay, 10% change: Found a plan in 0.1 seconds State-of-the-art planners vs. ours

12. Summary Introduced the ITT problem Defined objective functions to quantify network disruption Introduced the network topology planning domain Introduced novel domain-specific planners that significantly outperform existing planners on network A step towards making topology optimization work practically useful 12 Overlay Optimizer Change Planner (NEW!) “Too disruptive!” “Try this instead”