1. A system that routes a set of pairs of points during the design of an integrated circuit (IC) chip, comprising: a routing engine configured to search for a path to connect a current pair of points in the set of pairs of points; a routing database used by the routing engine, which keeps track of objects that can obstruct the routing of the current pair of points; and a satisfiability (SAT) solver capable of solving a set of constraints, which are associated with the routability of the set of pairs of points, wherein the SAT solver includes a SAT database which maintains the set of constraints and a current partial solution to the set of constraints, wherein the SAT database is configured to update the routing database if the current partial solution changes.