Even delta-matroids and the complexity of planar boolean CSPs

A. Kazda, V. Kolmogorov, M. Rolinek, ACM Transactions on Algorithms 15 (2019).


Journal Article | Published | English
Department
Abstract
The main result of this article is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all constraints are even Δ-matroid relations (represented by lists of tuples). As a consequence of this, we settle the complexity classification of planar Boolean CSPs started by Dvorak and Kupec. Using a reduction to even Δ-matroids, we then extend the tractability result to larger classes of Δ-matroids that we call efficiently coverable. It properly includes classes that were known to be tractable before, namely, co-independent, compact, local, linear, and binary, with the following caveat:We represent Δ-matroids by lists of tuples, while the last two use a representation by matrices. Since an n ×n matrix can represent exponentially many tuples, our tractability result is not strictly stronger than the known algorithm for linear and binary Δ-matroids.
Publishing Year
Date Published
2019-02-01
Journal Title
ACM Transactions on Algorithms
Volume
15
Issue
2
Article Number
22
IST-REx-ID

Cite this

Kazda A, Kolmogorov V, Rolinek M. Even delta-matroids and the complexity of planar boolean CSPs. ACM Transactions on Algorithms. 2019;15(2). doi:10.1145/3230649
Kazda, A., Kolmogorov, V., & Rolinek, M. (2019). Even delta-matroids and the complexity of planar boolean CSPs. ACM Transactions on Algorithms, 15(2). https://doi.org/10.1145/3230649
Kazda, Alexandr, Vladimir Kolmogorov, and Michal Rolinek. “Even Delta-Matroids and the Complexity of Planar Boolean CSPs.” ACM Transactions on Algorithms 15, no. 2 (2019). https://doi.org/10.1145/3230649.
A. Kazda, V. Kolmogorov, and M. Rolinek, “Even delta-matroids and the complexity of planar boolean CSPs,” ACM Transactions on Algorithms, vol. 15, no. 2, 2019.
Kazda A, Kolmogorov V, Rolinek M. 2019. Even delta-matroids and the complexity of planar boolean CSPs. ACM Transactions on Algorithms. 15(2).
Kazda, Alexandr, et al. “Even Delta-Matroids and the Complexity of Planar Boolean CSPs.” ACM Transactions on Algorithms, vol. 15, no. 2, 22, ACM, 2019, doi:10.1145/3230649.

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 1602.03124

Search this title in

Google Scholar