Abstract: Various computational systems may benefit from improvement in determining optimal allocation. For example certain social network advertisement systems may benefit from the use of hyperbolic embedding. A method, according to certain embodiments, can include obtaining a group of users as potential advertising targets. The method can also include mapping the group of users to a hyperbolic space. The method can further include expressing sets of users from the group of users as continuous subsets of the hyperbolic space. The method can additionally include determining influence for the expressed sets of users as sets. The method can also include allocating one or more of the sets to an advertising campaign based on the determined influence.

Abstract: Data tables in data warehouses are updated to minimize staleness and stretch of the data tables. New data is received from external sources and, in response, update requests are generated. Accumulated update requests may be batched. Data tables may be weighted to affect the order in which update requests are serviced.

Abstract: An example method involves for a first virtual private network (VPN) installed on a candidate hub router, selecting a first spoke-to-hub assignment solution having a first least memory utilization cost to assign the candidate hub router a quantity of first virtual private edge (VPE) routers serving the first VPN; for a second VPN installed on the candidate hub router, selecting a second spoke-to-hub assignment solution having a second least memory utilization cost to assign the candidate hub router a quantity of second VPE routers serving the second VPN; determining third least memory utilization costs to assign the candidate hub router to a quantity of the first VPE routers, and fourth least memory utilization costs to assign the candidate hub router to a quantity of the second VPE routers; and selecting the first or second spoke-to-hub assignment solution for the candidate hub router based on the least memory utilization costs.

Abstract: Minimum cost networks, such as fiber optic networks used in telecommunications, are obtained by defining available network elements having cost, required pairs, connectivity and penalty cost values and selecting from these available elements using an iterative rounding approximation method that constructs an LP relaxation incorporating the element parameters, finds an optimal basic solution, applies a selection criterion to pairs and edges in the optimal basic solution, and constructs a residual LP relaxation with selected pairs and edges. By fixing selected pairs and edges values to 1 in the residual LP, successive iterations of the method provide a design which is a 3-approximation solution to the minimum cost design problem.

Abstract: An example method involves for a first virtual private network (VPN) installed on a candidate hub router, selecting a first spoke-to-hub assignment solution having a first least memory utilization cost to assign the candidate hub router a quantity of first virtual private edge (VPE) routers serving the first VPN; for a second VPN installed on the candidate hub router, selecting a second spoke-to-hub assignment solution having a second least memory utilization cost to assign the candidate hub router a quantity of second VPE routers serving the second VPN; determining third least memory utilization costs to assign the candidate hub router to a quantity of the first VPE routers, and fourth least memory utilization costs to assign the candidate hub router to a quantity of the second VPE routers; and selecting the first or second spoke-to-hub assignment solution for the candidate hub router based on the least memory utilization costs.

Abstract: Minimum cost networks, such as fiber optic networks used in telecommunications, are obtained by defining available network elements having cost, required pairs, connectivity and penalty cost values and selecting from these available elements using an iterative rounding approximation method that constructs an LP relaxation incorporating the element parameters, finds an optimal basic solution, applies a selection criterion to pairs and edges in the optimal basic solution, and constructs a residual LP relaxation with selected pairs and edges. By fixing selected pairs and edges values to 1 in the residual LP, successive iterations of the method provide a design which is a 3-approximation solution to the minimum cost design problem.

Abstract: Minimum cost networks, such as fiber optic networks used in telecommunications, are obtained by defining available network elements having cost, required pairs, connectivity and penalty cost values and selecting from these available elements using an iterative rounding approximation method that constructs an LP relaxation incorporating the element parameters, finds an optimal basic solution, applies a selection criterion to pairs and edges in the optimal basic solution, and constructs a residual LP relaxation with selected pairs and edges. By fixing selected pairs and edges values to 1 in the residual LP, successive iterations of the method provide a design which is a 3-approximation solution to the minimum cost design problem.

Abstract: Methods and apparatus to implement scalable routing in network communication systems are disclosed. A disclosed example method involves selecting a plurality of virtual private networks in a communication network and selecting a candidate hub router from a plurality of routers in the communication network. The example method also involves determining a plurality of least memory utilization costs associated with assigning different quantities of spoke routers to the candidate hub router. Each of the least memory utilization costs and corresponding quantity of spoke routers is associated with a corresponding one of the plurality of virtual private networks. For each of the least memory utilization costs, a bandwidth usage of a corresponding one of the quantities of spoke routers is identified.

Abstract: Embodiments are directed to modeling propagation of an information item in an online social network. A quality value for the information item to be posted in the online social network is calculated, and the quality value is compared to a posting threshold value. The posting threshold value being determined based on a strategic user model. A propagation of the information item through the online social network is emulated based on the comparison.

Abstract: Methods and apparatus to implement scalable routing in network communication systems are disclosed. A disclosed example method involves selecting a plurality of virtual private networks in a communication network and selecting a candidate hub router from a plurality of routers in the communication network. The example method also involves determining a plurality of least memory utilization costs associated with assigning different quantities of spoke routers to the candidate hub router. Each of the least memory utilization costs and corresponding quantity of spoke routers is associated with a corresponding one of the plurality of virtual private networks. For each of the least memory utilization costs, a bandwidth usage of a corresponding one of the quantities of spoke routers is identified.

Abstract: Data tables in data warehouses are updated to minimize staleness and stretch of the data tables. New data is received from external sources and, in response, update requests are generated. Accumulated update requests may be batched. Data tables may be weighted to affect the order in which update requests are serviced.

Abstract: Minimum cost networks, such as fiber optic networks used in telecommunications, are obtained by defining available network elements having cost, required pairs, connectivity and penalty cost values and selecting from these available elements using an iterative rounding approximation method that constructs an LP relaxation incorporating the element parameters, finds an optimal basic solution, applies a selection criterion to pairs and edges in the optimal basic solution, and constructs a residual LP relaxation with selected pairs and edges. By fixing selected pairs and edges values to 1 in the residual LP, successive iterations of the method provide a design which is a 3-approximation solution to the minimum cost design problem.