In a large scale communication network, packets are transmitted from source nodes to destinations by going through several nodes on routes connecting them, because each node usually does not have a direct link to every node in the network. To maximize the usability in the network, the problems of selecting a transmission route for each connection request and of scheduling the link activations such that the total transmission time is minimized. This paper presents a four-stage approximation algorithm for the link scheduling problem (LSP) in a packet radio network, called MIPS-LSP, a MInimal-state Processing Search algorithm for LSP It is assumed that every link activation in the network is synchronously controlled by a single clock with a fixed time interval called a time slot. The first stage of MIPS-LSP computes the lower bound on the number of time slots for a given LSP instance. The second stage generates a link compatibility graph to represent the conflicts between links to be activated simultaneously. The third stage gives the initial state for search by a greedy method. The last stage iteratively searches a solution by a minimal-state evolution method The performance of the algorithm is verified through extensive simulations using benchmarks in literature.