In edge computing， computing resources are deployed at edge computing nodes closer to end users， and selecting the appropriate edge computing node deployment location from the candidate locations can enhance the node capacity and user Quality of Service （QoS） of edge computing services. However， there is less research on how to place edge computing nodes to reduce the cost of edge computing. In addition， there is no edge computing node deployment algorithm that can maximize the robustness of edge services while minimizing the deployment cost of edge computing nodes under the constraints of QoS factors such as the delay of edge services. To address the above issues， firstly， the edge computing node placement problem was transformed into a minimum dominating set problem with constraints by building a model about computing nodes， user transmission delay， and robustness. Then， the concept of overlapping domination was proposed， so that the network robustness was measured on the basis of overlapping domination， and an edge computing node placement algorithm based on overlapping domination was designed， namely CHAIN （edge server plaCement algoritHm based on overlAp domINation）. Simulation results show that CHAIN can reduce the system latency by 50.54% and 50.13% compared to the coverage oriented approximate algorithm and base station oriented random algorithm， respectively.