Exact Algorithms via Monotone Local Search
Fedor V. Fomin, Serge Gaspers, Daniel Lokshtanov, Saket Saurabh

TL;DR
This paper introduces a novel approach called monotone local search for designing exact exponential-time algorithms for subset problems, connecting parameterized algorithms with exponential algorithms and improving existing methods.
Contribution
It presents a general framework that leverages parameterized algorithms to enhance exponential-time algorithms for various subset problems, including derandomization techniques.
Findings
Improved exponential algorithms for d-Hitting Set, Feedback Vertex Set, and other problems.
Established a connection between parameterized and exponential algorithms.
Developed a derandomization method with subexponential overhead.
Abstract
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the family contains at least one set. Our approach is based on "monotone local search", where the goal is to extend a partial solution to a solution by adding as few elements as possible. More formally, in the extension problem we are also given as input a subset X of the universe and an integer k. The task is to determine whether one can add at most k elements to X to obtain a set in the (implicitly defined) family. Our main result is that an O*(c^k) time algorithm for the extension problem immediately yields a randomized algorithm for finding a solution of any size with running time O*((2-1/c)^n). In many cases, the extension problem can be reduced to…
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.
