Regional Categorization by Income Distribution in Tokyo Metropolitan Area

Abstract

In the MINMAX SET COVER RECONFIGURATION problem, given a set system F over a universe and its two covers C start and C goal of size k, we wish to transform C start into C goal by repeatedly adding or removing a single set of F while covering the universe in any intermediate state. Then, the objective is to minimize the maximize size of any intermediate cover during transformation. We prove that MINMAX SET COVER RECONFIGURATION and MINMAX DOMINATING SET RECONFIGURATION are PSPACEhard to approximate within a factor of 2 − 1 polyloglog N , where N is the size of the universe and the number of vertices in a graph, respectively, improving upon Ohsaka (SODA 2024) [Ohs24] and Karthik C. S. and Manurangsi (2023) [KM23]. This is the first result that exhibits a sharp threshold for the approximation factor of any reconfiguration problem because both problems admit a 2-factor approximation algorithm as per Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno (Theor. Comput. Sci., 2011) [IDHPSUU11]. Our proof is based on a reconfiguration analogue of the FGLSS reduction [FGLSS96] from Probabilistically Checkable Reconfiguration Proofs of Hirahara and Ohsaka (2024) [HO24]. We also prove that for any constant ε ∈ (0, 1), MINMAX HYPERGRAPH VERTEX COVER RECONFIGURATION on poly(ε −1 )-uniform hypergraphs is PSPACE-hard to approximate within a factor of 2 − ε.

Nurses’ Perceptions Regarding End-of-life Care for Individuals with Non-cancer Diseases on Non-invasive Positive Pressure Ventilation-dependent: A Qualitative and Descriptive Study

“…[ 3 ] Although later than other developed countries, Japan has begun to focus on palliative care for non-cancer patients. [ 4 ]…”