Abstract: System and method for efficiently carrying out a dynamic program for optimization in a graph. A method includes receiving a planar graph equipped with an embedding and edge cost function and a precision parameter, finding an edge subgraph of total cost for some constant, splitting the graph into a collection of subgraphs referred as slabs, for each slab, build a branch decomposition and solve a traveling salesman problem (TSP) exactly on it, returning a union of exact solutions on the slabs, and outputting a total cost.

Abstract: According to one method for approximating a network of terminals, a graph comprising nodes and edges connecting at least some of the nodes is received. The nodes include terminals and non-terminal nodes. The non-terminal nodes are each associated with a weight. The terminals are each initialized to a value. The values of the terminals are incremented by a given amount until the values of the terminals reach a sufficient amount to acquire at least one of the non-terminal nodes that connects at least two of the terminals based on the weight of the at least one of the non-terminal nodes. Upon the values of the terminals reaching the sufficient amount, the at least one of the non-terminal nodes and the edges connecting the at least one of the non-terminal nodes to the at least two of the terminals are acquired to form a connected component in the network of terminals.

Abstract: According to one method for approximating a network of terminals, a graph comprising nodes and edges connecting at least some of the nodes is received. The nodes include terminals and non-terminal nodes. The non-terminal nodes are each associated with a weight. The terminals are each initialized to a value. The values of the terminals are incremented by a given amount until the values of the terminals reach a sufficient amount to acquire at least one of the non-terminal nodes that connects at least two of the terminals based on the weight of the at least one of the non-terminal nodes. Upon the values of the terminals reaching the sufficient amount, the at least one of the non-terminal nodes and the edges connecting the at least one of the non-terminal nodes to the at least two of the terminals are acquired to form a connected component in the network of terminals.