Abstract: To answer if a user is a transitive member of a group efficiently, a method to maintain each node's ancestors or descendants is disclosed. The system maintains each node's ancestor paths or descendant paths and update affected nodes when a child node is added to or removed from the parent node. The affected nodes are the child and the child's descendants in the case of ancestor paths. The affected nodes are the parent and the parent's ancestors in the case of descendant paths. The node's ancestors or descendants are the unique nodes in the ancestor paths or descendant paths. Hybrid approaches can be used to reduce change volumes by skipping users.

Abstract: An energy harvester system including a primary energy collector (PEC), a cam gear ring, multiple secondary energy collectors (SEC), and a central gear is provided. The PEC and the SECs harness ambient motion energy. The PEC is attached to a support base member. The cam gear ring is operably engaged to the PEC and rotated by the PEC. The SECs are positioned in a space defined by the cam gear ring and rotated on receiving ambient motion energy. One SEC is unclamped from the support base member and slides towards the central gear when the cam gear ring contacts the SEC, while the other SECs are clamped on the support base member. The central gear operably engages with the unclamped SEC that slid towards the central gear and rotates with the unclamped SEC. The rotating central gear can be coupled to different power generating devices for generating electrical energy.