There is provided a system that uses a network matrix to carry out a search for shortest paths from a starting node included in a network having a plurality of nodes to other nodes. The network matrix includes link costs of links and each link has a root end that is a node included in the network and a tail end that is another node connected to the root end. The system includes a processor that includes a circuit for subtracting a lowest value from link costs of the subject links being searched that are included in the network matrix, a circuit for setting tail end node of a link out of the subject links whose link cost has become zero due to the subtracting as a reached node, a circuit for changing link costs of links included in the network matrix whose tail end nodes are the reached node to a value indicating exclusion from further search, and a circuit for setting values after the subtracting of link costs of the subject links whose link costs do not become zero due to the subtracting as link costs of links for a continued search.