1. Distributed optimization of multi-commodity routing in Software-Defined Networks
Mathieu Leconte, Ioannis Steiakogiannakis, Georgios Paschos
France Research Center, Huawei Technologies Co. Ltd
PGMO Days 2016

2. Optimization in multi-controller SDN
Inter-controller
communication protocols
(e.g., ONOS, OpenDayLight-SDNi)
“Public” memory
Private memory
Higher data rates & densification will carry the increased traffic at the access
Backhaul links will get congested (these include links from base stations to small cells)
Meeting throughput & latency targets of 5G requires mitigating such congestion
Is edge-caching suitable to solve these issues?
SDN moving towards partially distributed control logic
more distributed
Fast, optimal solutions
What can we achieve? Can we retain optimality & fast operation?
Optimal is too slow, operate in very sub-optimal regimes

3. Min-cost multi-commodity routing
Edge formulation
O(KV) constraints
O(KE) variables
Path formulation
O(K+E) constraints
many variables, but
O(K+E) active variables
Minimize cost
Serve demands
Capacity constraints
Flow conservation
Large problem size
V  1000 nodes, E  edges, K  demands
Sparse methods are required

4. Prior art & contributions
Fully centralized methods
interior point method  non-sparse
column generation (modified-cost shortest path) + simplex  sparse, fast in practice
Fully distributed methods
backpressure-like  too slow
Our contributions
Fast partially distributed methods preserving sparsity

5. Separating the problem into multiple domains
Minimize sum of intra-domain costs
Serve demands in source domain
Capacity constraints inside domains
Flow conservation at domain borders
Dantzig-Wolfe decomposition
Intra-domain problems + coupling constraints at domain borders

6. Handling flow agreement at domain borders
Penalize flow imbalance with Lagrange multipliers
Modified costs for intra-domain MCF
Subgradient method to update multipliers:
Flow imbalance  increase of multiplier
Exchange of border flow information between neighboring domains
Still decomposes into column generation + simplex
O(K+E(D)) active variables in each domain  sparse method in each domain

7. A sparse partially distributed solution
Inter-domain:
subgradient update of Lagrange multipliers
Lagrange multipliers for border edges
Intra-domain:
column generation + simplex for modified-cost MCF
Column generation + simplex inside domains
Fast and sparse
Subgradient between neighboring domains
Quite slow

8. Faster inter-domain updates
Replace subgradient with higher-order method
Non-smooth problem  no guarantee of speed-improvement
Augmented Lagrangian
Inter-cluster updates: Subgradient  parallel proximal ADMM
Intra-cluster modified MCF: linear simplex  quadratic simplex
More complex problem inside domains
We can still use column generation  still sparse
original cost
1st-order
flow-imbalance penalty
2nd-order flow-imbalance penalty

9. Fast & sparse partially distributed solution
Inter-domain:
parallel proximal ADMM update of Lagrange multipliers
Lagrange multipliers
+ neighboring flow
+ previous flow for border edges
Intra-domain:
column generation + quadratic simplex for modified-cost quadratic MCF
Much improved speed
Slightly less sparse

10. To sum-up Min-cost MCF = one basic problem for traffic engineering
Combination of centralized & distributed techniques
In practice, constrained paths (delay, node-inclusion, protections, optical,…)
SDN opens up new optimization challenges
“More optimal” solutions within reasonable time due to more centralization
Many traditional problems need to be revisited, many new problems as well