{"type":"ScholarlyArticle","title":"Maximum Satisfiability of Simple Temporal Problems","authors":[{"name":"Johannes K. Fichte","slug":"johannes-k-fichte","given":"Johannes K.","family":"Fichte","affiliation":""},{"name":"Johanna Groven","slug":"johanna-groven","given":"Johanna","family":"Groven","affiliation":""},{"name":"Peter Jonsson","slug":"peter-jonsson","given":"Peter","family":"Jonsson","affiliation":""},{"name":"Victor Lagerkvist","slug":"victor-lagerkvist","given":"Victor","family":"Lagerkvist","affiliation":""},{"name":"Jorke M. de Vlas","slug":"jorke-m-de-vlas","given":"Jorke M.","family":"de Vlas","affiliation":""}],"abstract":"The Simple Temporal Problem (STP) is a core framework for quantitative temporal constraints. As STP data can be inconsistent, we study MaxSTP: compute a maximum-cardinality consistent subset of constraints. This extension is NP-hard, and we analyze its parameterized complexity under measures that capture practically relevant instance features: the number of variables n (instance scale), the maximum coefficient magnitude k (numeric range), and structural parameters of the constraint graph such as treewidth tw (decomposability), and vertex cover size vc (density). We show that MaxSTP is W[1]-hard parameterized by n, implying that n and parameters that depend on n (including tw and vc) are insufficient for fixed-parameter tractability. For combined parameters, we give an O^*(k^n)-time algorithm, yielding single-exponential solvability for fixed k. While k+tw remains W[1]-hard, MaxSTP is in XP via an O^*((n * k)^tw) algorithm. Our results suggest that MaxSTP is often computationally harder than optimizing qualitative CSPs - we verify that many such problems (including RCC-8 and Allen's algebra) are FPT when parameterized by n or tw. However, we also demonstrate that FPT algorithms for MaxSTP are indeed possible but with other parameters such as k + vc.","doi":"10.24963/ijcai.2026/248","url":"https://ijcai.org/proceedings/2026/248","pdf":"https://ijcai.org/proceedings/2026/0248.pdf","markdown":"https://ijcai.org/proceedings/2026/248.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/248","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":248,"pages":{"first":2227,"last":2235},"keywords":["Constraint Satisfaction and Optimization: Constraint satisfaction","Constraint Satisfaction and Optimization: Constraint optimization problems"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}