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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2005.11307 |
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| _version_ | 1866929324521684992 |
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| author | Chen, Hubie |
| author_facet | Chen, Hubie |
| contents | The constraint satisfaction problem (CSP) on a finite relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the constraints; the surjective CSP is the variant where one decides the existence of a surjective satisfying assignment onto the universe of B.
We present an algebraic framework for proving hardness results on surjective CSPs; essentially, this framework computes global gadgetry that permits one to present a reduction from a classical CSP to a surjective CSP. We show how to derive a number of hardness results for surjective CSP in this framework, including the hardness of the disconnected cut problem, of the no-rainbow 3-coloring problem, and of the surjective CSP on all 2-element structures known to be intractable (in this setting). Our framework thus allows us to unify these hardness results, and reveal common structure among them; we believe that our hardness proof for the disconnected cut problem is more succinct than the original. In our view, the framework also makes very transparent a way in which classical CSPs can be reduced to surjective CSPs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_11307 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Algebraic Global Gadgetry for Surjective Constraint Satisfaction Chen, Hubie Computational Complexity The constraint satisfaction problem (CSP) on a finite relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the constraints; the surjective CSP is the variant where one decides the existence of a surjective satisfying assignment onto the universe of B. We present an algebraic framework for proving hardness results on surjective CSPs; essentially, this framework computes global gadgetry that permits one to present a reduction from a classical CSP to a surjective CSP. We show how to derive a number of hardness results for surjective CSP in this framework, including the hardness of the disconnected cut problem, of the no-rainbow 3-coloring problem, and of the surjective CSP on all 2-element structures known to be intractable (in this setting). Our framework thus allows us to unify these hardness results, and reveal common structure among them; we believe that our hardness proof for the disconnected cut problem is more succinct than the original. In our view, the framework also makes very transparent a way in which classical CSPs can be reduced to surjective CSPs. |
| title | Algebraic Global Gadgetry for Surjective Constraint Satisfaction |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2005.11307 |