https://github.com/madvorak/vcsp
General-Valued Constraint Satisfaction Problems — playground for experiments preceding my contribution to Mathlib
https://github.com/madvorak/vcsp
combinatorial-optimization constraint-satisfaction-problem lean4 linear-programming symmetric-fractional-polymorphism
Last synced: 4 months ago
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General-Valued Constraint Satisfaction Problems — playground for experiments preceding my contribution to Mathlib
- Host: GitHub
- URL: https://github.com/madvorak/vcsp
- Owner: madvorak
- License: apache-2.0
- Created: 2023-10-06T15:38:37.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2024-04-12T20:44:52.000Z (about 1 year ago)
- Last Synced: 2024-04-12T23:06:14.905Z (about 1 year ago)
- Topics: combinatorial-optimization, constraint-satisfaction-problem, lean4, linear-programming, symmetric-fractional-polymorphism
- Language: Lean
- Homepage:
- Size: 492 KB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# General-Valued Constraint Satisfaction Problems
This is a playground for experiments preceding our contribution to the [Lean 4](https://github.com/leanprover/lean4) version of [Mathlib](https://github.com/leanprover-community/mathlib4).
[Permalink to the definition of VCSP in Mathlib](https://github.com/leanprover-community/mathlib4/blob/3e51ad145c59d7e879943907172a6c5a89d6420c/Mathlib/Combinatorics/Optimization/ValuedCSP.lean#L39)
Our long-term goal is to formalize the dichotomy for fixed-template finite-valued constraint satisfaction problems [Thapper, Živný, Kolmogorov] while exploring potential generalizations (infinite domains, partially ordered codomains, and more).
## Results (please see the definitions in [ValuedCSP.lean](https://github.com/leanprover-community/mathlib4/blob/master/Mathlib/Combinatorics/Optimization/ValuedCSP.lean) first)
* [If a VCSP template over LinearOrderedCancelAddCommMonoid can express MaxCut, it cannot have any commutative fractional polymorphism.](https://github.com/madvorak/vcsp/blob/d9e00ac4cc6f790ec675b4c996cc56a4fd726a0d/VCSP/Hardness.lean#L70)
* [Basic LP relaxation for VCSP over any OrderedRing of CharZero is valid.](https://github.com/madvorak/vcsp/blob/d9e00ac4cc6f790ec675b4c996cc56a4fd726a0d/VCSP/LinearRelaxation.lean#L261)
* [If a VCSP template over ℚ has symmetric fractional polymorphisms of all arities, then Basic LP relaxation is tight.](https://github.com/madvorak/vcsp/blob/d9e00ac4cc6f790ec675b4c996cc56a4fd726a0d/VCSP/LinearRelaxationAndSFP.lean#L398)
## Mathlib contributions that stem from this project
### Pull requests (these PRs are compatible with each other)
* https://github.com/leanprover-community/mathlib4/pull/7404
* https://github.com/leanprover-community/mathlib4/pull/7893
* https://github.com/leanprover-community/mathlib4/pull/7894
* https://github.com/leanprover-community/mathlib4/pull/8707
* https://github.com/leanprover-community/mathlib4/pull/9072
* https://github.com/leanprover-community/mathlib4/pull/9307
* https://github.com/leanprover-community/mathlib4/pull/9652
* https://github.com/leanprover-community/mathlib4/pull/9838
* https://github.com/leanprover-community/mathlib4/pull/10297
* https://github.com/leanprover-community/mathlib4/pull/10379
* https://github.com/leanprover-community/mathlib4/pull/11689
* https://github.com/leanprover-community/mathlib4/pull/12806
* https://github.com/leanprover-community/mathlib4/pull/12901
* https://github.com/leanprover-community/mathlib4/pull/12903
* https://github.com/leanprover-community/mathlib4/pull/12911
* https://github.com/leanprover-community/mathlib4/pull/13167
### Proposals for Linear Programming (these PRs are incompatible with each other)
* https://github.com/leanprover-community/mathlib4/pull/7386
* https://github.com/leanprover-community/mathlib4/pull/9693
* https://github.com/leanprover-community/mathlib4/pull/10026
* https://github.com/leanprover-community/mathlib4/pull/10159