Abstract: A method, system and product for using multiple packing stations in delivery of goods. A packing scheme is determined for an order based on an optimality criteria, the scheme comprising a division of a set of items between packing stations, whereby defining one or more subsets of the set of items. The packing scheme further comprising an ordering of the one or more subsets and packing stations paired therewith, by which ordering the paired packing stations are to be utilized for packing the set of items and transporting thereof to the destination, wherein in each packing station, a respective portion of the set of items is to be packed and transported therefrom. Responsive to the optimality criteria being met, instructions for executing the order are issued, whereby the set of items are packed and transported according to the packing scheme.

Abstract: An inventory handling system includes multiple shelving units for mounting over a horizontal floor. Each shelving unit contains a vertical array of shelves on which containers are placed. One or more floor robots travel among the shelving units along first paths on the floor. One or more lift robots move independently of the floor robots along second paths in a vertical plane over vertical faces of the shelving units, and transfer the containers between the shelves and the floor robots.

Abstract: An inventory handling system includes multiple shelving units for mounting over a horizontal floor. Each shelving unit contains a vertical array of shelves on which containers are placed. One or more floor robots travel among the shelving units along first paths on the floor. One or more lift robots move independently of the floor robots along second paths in a vertical plane over vertical faces of the shelving units, and transfer the containers between the shelves and the floor robots.

Abstract: A method, system and product for using multiple packing stations in delivery of goods. A packing scheme is determined for an order based on an optimality criteria, the scheme comprising a division of a set of items between packing stations, whereby defining one or more subsets of the set of items. The packing scheme further comprising an ordering of the one or more subsets and packing stations paired therewith, by which ordering the paired packing stations are to be utilized for packing the set of items and transporting thereof to the destination, wherein in each packing station, a respective portion of the set of items is to be packed and transported therefrom. Responsive to the optimality criteria being met, instructions for executing the order are issued, whereby the set of items are packed and transported according to the packing scheme.

Abstract: An inventory handling system (20, 150) includes multiple shelving units (22) for mounting over a horizontal floor (24). Each shelving unit contains a vertical array of shelves (28) on which containers (30) are placed. One or more floor robots (36) travel among the shelving units along first paths on the floor. One or more lift robots (32, 80, 120, 152) move independently of the floor robots along second paths in a vertical plane over vertical faces of the shelving units, and transfer the containers between the shelves and the floor robots.

Abstract: An inventory handling system (20, 150) includes multiple shelving units (22) for mounting over a horizontal floor (24). Each shelving unit contains a vertical array of shelves (28) on which containers (30) are placed. One or more floor robots (36) travel among the shelving units along first paths on the floor. One or more lift robots (32, 80, 120, 152) move independently of the floor robots along second paths in a vertical plane over vertical faces of the shelving units, and transfer the containers between the shelves and the floor robots.

Abstract: Function properties may be approximated using an expander graph. For example, an approximate average of a function may be determined by randomly exploring an expander graph. Values of the function are associated with vertices of the expander graph. The expander graph is randomly explored by traversing edges and encountering vertices. The exploration may comprise a crawl, a walk, and so forth. An approximate average of the function is determined based on the function values that are associated with encountered vertices.

Abstract: Pscudorandom numbers may be generated from input seeds using expander graphs. Expander graphs are a collection of vertices that are interconnected via edges. Generally, a walk around an expander graph is determined responsive to an input seed, and a pseudorandom number is produced based on vertex names. Specifically, a next edge, which is one of multiple edges emanating from a current vertex, is selected responsive to an extracted seed chunk. The next edge is traversed to reach a next vertex. The name of the next vertex is ascertained and used as a portion of the pseudorandom number being produced by the walk around the expander graph.

Abstract: Hash function constructions from expander graphs are described. In one aspect, an expander graph is walked to compute a hash function. The expander graph is walked using respective subsets of an input message. A label of a last vertex walked is an output of the hash function.