The problem of placing or selecting sensors and control nodes plays a pivotal role in the operation of dynamic networks. This paper proposes optimal algorithms and heuristics to solve the Simultaneous Sensor and Actuator Selection Problem (SSASP) in linear dynamic networks. In particular, a sufficiency condition of static output feedback stabilizability is used to obtain the minimal set of sensors and control nodes needed to stabilize an unstable network. We then show that SSASP can be written as a mixed-integer nonconvex problem. To solve this nonconvex combinatorial problem, three methods based on (i) mixed-integer nonlinear programming, (ii) binary search algorithms, and (iii) simple heuristics are proposed. The first method yields optimal solutions to SSASP given that some constants are appropriately selected. The second method requires a database of binary sensor/actuator combinations, returns optimal solutions, and necessitates no tuning parameters. The third approach is a heuristic that yields suboptimal solutions but is computationally attractive. The theoretical properties of these methods are discussed and numerical tests on dynamic networks showcase the trade-off between optimality and computational time. (C) 2019 Elsevier Ltd. All rights reserved.