Planning the Transformation of

Network TopologiesYoung Yoon1, Nathan Robinson2, Vinod Muthusamy3,

Sheila McIlraith2, Hans-Arno Jacobsen2

1Samsung Electronics, 2University of Toronto,3IBM T.J. Watson Research Center

The Need for Transforming a Topology

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Old topology New topology

Message stream

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Removable edge Goal edge

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• 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

Transform “incrementally” using primitive transformation operators

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Initial state Goal state

SHIFT(i, j, k)

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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

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Many Ways to Transform Incrementally

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Start S1 S2 S3 S4 S5

S6 S7Goal

Removable edge

Goal edge

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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 (vi, vj) E , where v∈ i and vj V∈

• T = < TS, TG, O >– TS is the initial topology

– TG is the goal topology– O is a set of transformation operations

• Removable edge: e in a topology TS and not in TG

• Plan: A sequence of transformation operations that achieves TG from TS with the least cost

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The Key Domain Knowledge:End-to-End Path of a Goal Edge

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Shift the removable edge on the end-to-end path between the nodes that constitute the goal edge.

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Breaking into Sub-Problems to Assess Disruption to Message Flows

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Start Topology15

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Goal Topology

Sub-problem 1

Sub-problem 2

The Effect of Sub-problem Solving Ordering

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Incurs11 routingstate updates

Sub-problem 1 Sub-problem 2

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Incurs5 routingstate updates

Sub-problem 2 Sub-problem 1

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

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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

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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 Size Solution 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 system400-node overlay, 10% change: Found a planin 0.1 seconds

State-of-the-art planners vs. ours

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

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Overlay Optimizer

ChangePlanner(NEW!)

“Too disruptive!”

“Try this instead”