A Logic-Based Benders Decomposition Approach for the VNF Assignment Problem
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Bibliographic record
Abstract
Middleboxes have gained popularity due to the significant value-added services these network elements provide to traffic flows, in terms of enhanced performance and security. Policy-aware traffic flows usually need to traverse multiple middleboxes in a predefined order to satisfy their associated policy, also known as Service Function Chaining. Typically, Middleboxes run on specialized hardware, which make them highly inflexible to handle the unpredictable and fluctuating-nature of traffic, and contribute to significant capital and operational expenditures (Cap-ex and Op-ex) to provision, accommodate, and maintain them. Network Function Virtualization is a promising technology with the potential to tackle the aforementioned limitations of hardware middleboxes. Yet, NFV is still in its infancy, and there exists several technical challenges that need to be addressed, among which, the Virtual Network Function assignment problem tops the list. The VNF assignment problem stems from the newly gained flexibility in instantiating VNFs (on-demand) anywhere in the network. Subsequently, network providers must decide on the optimal placement of VNF instances which maximizes the number of admitted policy-aware traffic flows across their network. Existing work consists of Integer Linear Program (ILP) models, which are fairly unscalable, or heuristic-based approaches with no guarantee on the quality of the obtained solutions. This work proposes a novel Logic-Based Benders Decomposition (LBBD) based approach to solve the VNF assignment problem. It consists of decomposing the problem into two subproblems: a master and a subproblem; and at every iteration constructive Benders cuts are introduced to the master to tighten its search space. We compared the LBBD approach against the ILP and a heuristic method, and we show that our approach achieves the optimal solution (as opposed to heuristic-based methods) 700 times faster than the ILP.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.003 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it