{"type":"ScholarlyArticle","title":"Parameterized Local Search for Max c-Cut","authors":[{"name":"Jaroslav Garvardt","slug":"jaroslav-garvardt","given":"Jaroslav","family":"Garvardt","affiliation":"Friedrich Schiller University Jena , Institute of Computer Science , Germany"},{"name":"Niels Grüttemeier","slug":"niels-gruttemeier","given":"Niels","family":"Grüttemeier","affiliation":"Fraunhofer Institute of Optronics , System Technologies and Image Exploitation , Germany"},{"name":"Christian Komusiewicz","slug":"christian-komusiewicz","given":"Christian","family":"Komusiewicz","affiliation":"Friedrich Schiller University Jena , Institute of Computer Science , Germany"},{"name":"Nils Morawietz","slug":"nils-morawietz","given":"Nils","family":"Morawietz","affiliation":"Friedrich Schiller University Jena , Institute of Computer Science , Germany"}],"abstract":"In the NP-hard Max c-Cut problem, one is given an undirected edge-weighted graph G and wants to color the vertices of G with c colors such that the total weight of edges with distinctly colored endpoints is maximal. The case with c=2 is the famous Max Cut problem. To deal with the NP-hardness of this problem, we study parameterized local search algorithms. More precisely, we study LS-Max c-Cut where we are additionally given a vertex coloring f and an integer k and the task is to find a better coloring f' that differs from f in at most k entries, if such a coloring exists; otherwise, f is k-optimal. We show that LS-Max c-Cut presumably cannot be solved in g(k) · nᴼ⁽¹⁾ time even on bipartite graphs, for all c ≥ 2. We then show an algorithm for LS-Max c-Cut with running time O((3eΔ)ᵏ · c · k³ · Δ · n), where Δ is the maximum degree of the input graph. Finally, we evaluate the practical performance of this algorithm in a hill-climbing approach as a post-processing for state-of-the-art heuristics for Max c-Cut. We show that using parameterized local search, the results of this heuristic can be further improved on a set of standard benchmark instances.","doi":"10.24963/ijcai.2023/620","url":"https://ijcai.org/proceedings/2023/620","pdf":"https://ijcai.org/proceedings/2023/0620.pdf","markdown":"https://ijcai.org/proceedings/2023/620.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/620","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Search","track":"Main Track","number":620,"pages":{"first":5586,"last":5594},"keywords":["Search: S: Local search"],"videos":[],"references":[{"position":1,"raw":"[Arbour et al., 2021] David Arbour, Drew Dimmery, and Anup B. 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