The component-hypertree is a data structure that generalizes the concept of component-tree to multiple (increasing) neighborhoods. However, construction of a component-hypertree is costly because it needs to process a high number of neighbors. In this article, we present some properties used to obtain optimized neighborhoods for component-hypertree computation. Using these properties, we explore a new strategy to obtain neighboring elements based on hierarchy of partitions, leading to a more efficient algorithm with the drawback of a slight loss of precision on the distance of merged nodes.