Abstract: Content item presentation slots (e.g., advertisement slots) can be grouped into a slot group so that more than one presenter (e.g., advertiser) can share a corresponding number of slots on the publisher's property over a defined time period. The presenters can be scheduled to the slots within the slot group to maximize a performance measurement (e.g., number of clicks) that each presenter realizes according to budget constraints that are defined by the presenters.

Abstract: A computer implemented method finds a path having a minimal expected cost through a network of nodes connected by arcs, in which the path is from a source node to a destination node, and in which a traversal time for traversing each arc is a random variable. An expected cost of traversing each possible path from the source node to the destination node is determined as an average value of a nonlinear cost function applied to each possible total travel time for traversing the path. The expected cost is weighted according to a probability of each possible total travel time. For each node in the network and for each possible time to start, a particular path from the source node to the node having a minimal expected cost and an optimal time to start on that path is determined.

Abstract: Content item presentation slots (e.g., advertisement slots) can be grouped into a slot group so that more than one presenter (e.g., advertiser) can share a corresponding number of slots on the publisher's property over a defined time period. The presenters can be scheduled to the slots within the slot group to maximize a performance measurement (e.g., number of clicks) that each presenter realizes according to budget constraints that are defined by the presenters.

Abstract: A method finds an optimal path from a source to a destination. The possible paths from the source to the destination are represented as a stochastic graph of nodes connected by edges. Each edge has an independent probability distribution over a cost of the edge. A constraint for reaching the destination is defined. The graph is reduced to a relatively small set of deterministic minimum cost problems, which can be solved to determine an optimal path that maximizes a probability of reaching the destination within the constraint.

Abstract: A method finds an optimal path from a source to a destination. The possible paths from the source to the destination are represented as a stochastic graph of nodes connected by edges. Each edge has an independent probability distribution over a cost of the edge. A constraint for reaching the destination is defined. The graph is reduced to a relatively small set of deterministic minimum cost problems, which can be solved to determine an optimal path that maximizes a probability of reaching the destination within the constraint.

Abstract: A computer implemented method finds a path having a minimal expected cost through a network of nodes connected by arcs, in which the path is from a source node to a destination node, and in which a traversal time for traversing each arc is a random variable. An expected cost of traversing each possible path from the source node to the destination node is determined as an average value of a nonlinear cost function applied to each possible total travel time for traversing the path. The expected cost is weighted according to a probability of each possible total travel time. For each node in the network and for each possible time to start, a particular path from the source node to the node having a minimal expected cost and an optimal time to start on that path is determined.