Conference item
PTAS for sparse general-valued CSPs
- Abstract:
- We study polynomial-time approximation schemes (PTASes) for constraint satisfaction problems (CSPs) such as Maximum Independent Set or Minimum Vertex Cover on sparse graph classes.Baker’s approach gives a PTAS on planar graphs, excluded-minor classes, and beyond. For Max-CSPs, and even more generally, maximisation finite-valued CSPs (where constraints are arbitrary non-negative functions), Romero, Wrochna, and Živný [SODA’21] showed that the Sherali-Adams LP relaxation gives a simple PTAS for all fractionally-treewidth-fragile classes, which is the most general "sparsity" condition for which a PTAS is known. We extend these results to general-valued CSPs, which include "crisp" (or "strict") constraints that have to be satisfied by every feasible assignment. The only condition on the crisp constraints is that their domain contains an element which is at least as feasible as all the others (but possibly less valuable).For minimisation general-valued CSPs with crisp constraints, we present a PTAS for all Baker graph classes — a definition by Dvořák [SODA’20] which encompasses all classes where Baker’s technique is known to work, except for fractionally-treewidth-fragile classes. While this is standard for problems satisfying a certain monotonicity condition on crisp constraints, we show this can be relaxed to diagonalisability — a property of relational structures connected to logics, statistical physics, and random CSPs.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
-
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(Preview, Accepted manuscript, 393.2KB, Terms of use)
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- Publisher copy:
- 10.1109/LICS52264.2021.9470599
Authors
- Publisher:
- IEEE
- Host title:
- 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- Pages:
- 1-11
- Publication date:
- 2021-07-07
- Acceptance date:
- 2021-04-01
- Event title:
- ACM/IEEE 36th Annual Symposium on Logic in Computer Science (LICS 2021)
- Event location:
- Online
- Event website:
- http://easyconferences.eu/lics2021/
- Event start date:
- 2021-06-29
- Event end date:
- 2021-07-02
- DOI:
- EISBN:
- 9781665448956
- ISBN:
- 9781665448963
- Language:
-
English
- Keywords:
- Pubs id:
-
1170315
- Local pid:
-
pubs:1170315
- Deposit date:
-
2021-04-03
Terms of use
- Copyright holder:
- IEEE
- Copyright date:
- 2021
- Rights statement:
- © 2021 IEEE.
- Notes:
- This paper was presented at the ACM/IEEE 36th Annual Symposium on Logic in Computer Science (LICS 2021), 29 June – 2 July 2021, Online. The final version is available online from IEEE at: https://doi.org/10.1109/LICS52264.2021.9470599.
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