In　modern　circuit　designs,　standard　cells　are　designed　with　different　heights　based　on　the　power,　area,　and　other　characteristics　to　address　various　design　requirements.　For　those　cells　with　different　heights,　in　particular,　there　are　inter-cell　diffusion　steps　if　the　diffusion　heights　of　neighboring　cells　are　different,　called　the　neighbor　diffusion　effect　(NDE)　which　has　become　critical　in　advanced　technology　nodes.　In　this　paper,　we　present　a　Hamiltonian-path-based　mixed-cell-height　legalization　algorithm　for　NDE　mitigation.　We　first　present　a　row　assignment　method　considering　both　cell　displacements　and　diffusion　steps　to　assign　cells　to　their　desired　rows　that　meet　the　power-rail　alignment　constraints.　Then,　we　propose　a　Hamiltonian-path-based　diffusion-step　reduction　method　to　effectively　reduce　the　NDE　violations　while　preserving　the　global　placement　solution.　Particularly,　we　develop　a　2-approximation　algorithm　to　find　a　minimum　weight　Hamiltonian　path　connecting　two　vertices,　and　a　1.5-approximation　algorithm　to　find　a　minimum　weight　Hamiltonian　path　with　a　specified　end　vertex.　Finally,　we　present　an　NDE-aware　legalization　method　with　design　compaction　to　resolve　overlaps　and　NDE　violations.　Experimental　results　show　that　our　algorithm　can　resolve　all　NDE　violations　without　any　area　overhead　in　reasonable　runtime.　©　2020　IEEE.