The paradigm shift toward SDN has exhibited the following trends: (1) relying on a centralized and more powerful controller to make intelligent decisions, and (2) allowing a set of relatively dumb switches to route packets. Therefore, efficiently looking up the flowtables in forwarding switches to guarantee low latency becomes a critical issue. In this paper, following the similar paradigm, we propose a new routing scheme called KeySet which is flowtable-free and enables constant-time switching at the forwarding switches. Instead of looking up long flowtables, KeySet relies on a residual system to quickly calculate routing paths. A switch only needs to do simple modular arithmetics to obtain a packet's forwarding output port. Moreover, KeySet has a nice fault-tolerant capability because in many cases the controller does not need to update flowtables at switches when a failure occurs. We validate KeySet through extensive simulations by using general as well as Facebook fat-tree topologies. The results show that the KeySet outperforms the KeyFlow scheme  by at least 25% in terms of the length of the forwarding label. Moreover, we show that KeySet is very efficient when applied to fat-trees.