# 2nd research iteration results & roadmapping
###### tags: `gitcoin` `Reports`
:::info
Updated by December 2021
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*Authors: Danilo Lessa Bernardineli*
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## Results under the original scope
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- The definitions & methodology of the research plan were sucessfully implemented
- This includes creating rewiring optimizers based on Hill Climbing and Simulated Annealing that were pushed to the NetworkX module
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<sup><sub>*Source: https://github.com/gitcoinco/gitcoin_cadcad_model/tree/main/optimality_gap*</sub></sup>
![](https://i.imgur.com/oLryk5R.png)
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- We have the capacity of knowing the Optimality Gap under limited circumstances
- The current capacity is limited due to the complexity factor of the current QF algorithm implementation, which is quadratic: $O(n^2)$
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<sup><sub>*Source: https://github.com/gitcoinco/gitcoin_cadcad_model/blob/main/optimality_gap.ipynb*
![](https://i.imgur.com/BnNOGqM.png)</sub></sup>
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- The further testing of the proposed hypothesis is blocked by further R&D
- Large-scale analysis and simulations requires potentially tens of thousands of evaluations, or the adoption of better heuristics. A more comprehensive mathematical description of the algorithm could also create shortcuts.
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<sup><sub>*Source: https://github.com/gitcoinco/gitcoin_cadcad_model/blob/main/optimality_gap.ipynb*
![](https://i.imgur.com/jNJ1XPL.png)</sub></sup>
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## Results Outside the scope
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- We've written drafts of mathematical specs that could result in drastic improvements to QF evaluation performance on operations and research.
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<sup><sub>*Source: https://hackmd.io/7HYPPp7zQcShQLrKQ2KOxQ?view#Simple-Quadratic-Match*</sub></sup>
![](https://i.imgur.com/ELASsRS.png)
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- We've tested the effect of attack vectors under limited subsets of the Gitcoin Grants data.
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<sup><sub>*Source: https://github.com/jiajia20/GitCoin_attack/blob/main/attack_vector.ipynb*</sub></sup>
![](https://i.imgur.com/zcy1bKL.png)
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<sup><sub>*Source: https://github.com/gitcoinco/gitcoin_cadcad_model/blob/main/attack_vector_ab_test.ipynb*</sub></sup>
![](https://i.imgur.com/tsewgPN.png)
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- We've promoted public research interest on Gitcoin and Quadratic Funding.
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<sup><sub>*Source: https://www.notion.so/Gitcoin-Modelling-Co-Lab-TL-DR-dba6e25863a1413a81e75f989f4a1f67*</sub></sup>
![](https://i.imgur.com/PJVUHFG.png)
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## Next Steps
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- Improving the scalability of the Optimality Gap calculations
- Starting point heuristics based on attack vectors
- Iterative rewiring algorithm for QF
- Linear Algebra formalism for QF
- Researching analytical solutions for optimizing QF
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- Investigating the effect of attack vectors under a range of scenarios on synthetic / subset scenarios
- What if the distribution of the amounts change?
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- Searching for attack vector patterns on synthetic / subset scenarios
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