In the \(\textsc {Max} r\text {-}\textsc {SAT}{}\) problem, input is a CNF formula with n variables where each clause disjunction of at most r literals. The objective to compute an assignment which satisfies as many clauses possible. While there are polynomial-time approximation algorithms for this we take viewpoint space complexity following [Biswas et al., Algorithmica 2021] and design sublin...

n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for $%mathcal{P}_{0}(X)$-valued set multifunctions ($X$ being a linear,topological space), in order to obtain Egoroff and Lusin type theorems forset multifunctions in the Vietoris hypertopology. Some mathematicalapplications are established and several physical implications of thema...