Multiprotocol Label Switching (MPLS) enables the deployment of Internet traffic engineering to be sim- ple and efficient by using explicit routing of Label Switching Path (LSP). Hence, the LSP routing algorithmbecomes the core and hot topic of traffic engineering. This paper analyzes the key ideas of Minimum InterferenceRouting Algorithm (MIRA) for LSP routing and then surveys the current improved schemes of MIRA. According totheir technical methods, they are classified as reconfirming critical links class, utilizing traffic profile informationclass, adding admission control class, and solving multiple Quality of Service constraints class. After the key idea is analyzed for each class, their typical algorithms are presented and their advantages, suitable environments and shortcomings with a detailed comprehensive comparison are discussed. The end of the paper points out the future research field for the min- imum interference routing problem.