On the complexity of Sandwich Problems for $M$-partitions
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918330939473920 |
|---|---|
| author | Barsukov, Alexey Guzmán-Pro, Santiago |
| author_facet | Barsukov, Alexey Guzmán-Pro, Santiago |
| contents | We present a structural classification of constraint satisfaction problems (CSP) described by reflexive complete $2$-edge-coloured graphs. In particular, this classification extends the structural dichotomy for graph homomorphism problems known as the Hell--Nešetřil theorem (1990). Our classification is also efficient: we can check in polynomial time whether the CSP of a reflexive complete $2$-edge-coloured graph is in P or NP-complete, whereas for arbitrary $2$-edge-coloured graphs, this task is NP-complete. We then apply our main result in the context of matrix partition problems and sandwich problems. Firstly, we obtain one of the few algorithmic solutions to general classes of matrix partition problems. And secondly, we present a P vs. NP-complete classification of sandwich problems for matrix partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09576 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the complexity of Sandwich Problems for $M$-partitions Barsukov, Alexey Guzmán-Pro, Santiago Computational Complexity Discrete Mathematics Combinatorics 05C15, 05C60 G.2.2; F.2.2 We present a structural classification of constraint satisfaction problems (CSP) described by reflexive complete $2$-edge-coloured graphs. In particular, this classification extends the structural dichotomy for graph homomorphism problems known as the Hell--Nešetřil theorem (1990). Our classification is also efficient: we can check in polynomial time whether the CSP of a reflexive complete $2$-edge-coloured graph is in P or NP-complete, whereas for arbitrary $2$-edge-coloured graphs, this task is NP-complete. We then apply our main result in the context of matrix partition problems and sandwich problems. Firstly, we obtain one of the few algorithmic solutions to general classes of matrix partition problems. And secondly, we present a P vs. NP-complete classification of sandwich problems for matrix partitions. |
| title | On the complexity of Sandwich Problems for $M$-partitions |
| topic | Computational Complexity Discrete Mathematics Combinatorics 05C15, 05C60 G.2.2; F.2.2 |
| url | https://arxiv.org/abs/2602.09576 |