{"ID":2835360,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.22914","arxiv_id":"2511.22914","title":"Towards an algebraic approach to the reconfiguration CSP","abstract":"This paper investigates the reconfiguration variant of the Constraint Satisfaction Problem (CSP), referred to as the Reconfiguration CSP (RCSP). Given a CSP instance and two of its solutions, RCSP asks whether one solution can be transformed into the other via a sequence of intermediate solutions, each differing by the assignment of a single variable. RCSP has attracted growing interest in theoretical computer science, and when the variable domain is Boolean, the computational complexity of RCSP exhibits a dichotomy depending on the allowed constraint types. A notable special case is the reconfiguration of graph homomorphisms -- also known as graph recoloring -- which has been studied using topological methods. We propose a novel algebraic approach to RCSP, inspired by techniques used in classical CSP complexity analysis. Unlike traditional methods based on total operations, our framework employs partial operations to capture a reduction involving equality constraints. This perspective facilitates the extension of complexity results from Boolean domains to more general settings, demonstrating the versatility of partial operations in identifying tractable RCSP instances.","short_abstract":"This paper investigates the reconfiguration variant of the Constraint Satisfaction Problem (CSP), referred to as the Reconfiguration CSP (RCSP). Given a CSP instance and two of its solutions, RCSP asks whether one solution can be transformed into the other via a sequence of intermediate solutions, each differing by the...","url_abs":"https://arxiv.org/abs/2511.22914","url_pdf":"https://arxiv.org/pdf/2511.22914v2","authors":"[\"Kei Kimura\"]","published":"2025-11-28T06:36:53Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}