On Exact Algorithms for Permutation CSP
Eun Jung Kim, Daniel Goncalves

TL;DR
This paper proves that solving the Arity 4 Permutation CSP problem cannot be done faster than $2^{o(n ext{log}n)}$ time unless ETH fails, closing a significant complexity gap.
Contribution
It establishes a tight lower bound for the complexity of Arity 4 Permutation CSP, showing no significantly faster algorithms exist under ETH.
Findings
Proves no $2^{o(n ext{log}n)}$ algorithm for Arity 4 Permutation CSP unless ETH fails.
Closes the complexity gap for Permutation CSP with arity 4 and above.
Highlights the computational difficulty of higher-arity permutation problems.
Abstract
In the Permutation Constraint Satisfaction Problem (Permutation CSP) we are given a set of variables and a set of constraints C, in which constraints are tuples of elements of V. The goal is to find a total ordering of the variables, , which satisfies as many constraints as possible. A constraint is satisfied by an ordering when . An instance has arity if all the constraints involve at most elements. This problem expresses a variety of permutation problems including {\sc Feedback Arc Set} and {\sc Betweenness} problems. A naive algorithm, listing all the permutations, requires time. Interestingly, {\sc Permutation CSP} for arity 2 or 3 can be solved by Held-Karp type algorithms in time , but no algorithm is known for arity at least 4 with running…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsgraph theory and CDMA systems · Advanced Graph Theory Research · Genome Rearrangement Algorithms
