The　obstacle-avoiding　rectilinear　Steiner　minimal　tree　(OARSMT)　problem　is　a　hot　topic　in　very-large-scale　integration　physical　design.　In　practice,　most　of　the　obstacles　occupy　the　device　layer　and　certain　lower　metal　layers.　Therefore,　we　can　place　wires　on　top　of　the　obstacles.　To　maximize　routing　resources　over　obstacles,　we　propose　a　heuristic　for　constructing　a　rectilinear　Steiner　tree　with　slew　constraints.　Our　algorithm　adopts　an　extended　rectilinear　full　Steiner　tree　grid　as　the　routing　graph.　We　mark　two　types　of　Steiner　point　candidates,　which　are　used　for　constructing　Steiner　trees　and　refining　solutions.　A　shortest　path　heuristic　variant　is　designed　for　constructing　Steiner　trees　and　it　takes　into　account　slew　constraint　by　inhibiting　growth.　Furthermore,　we　use　a　pre-computed　strategy　to　avoid　calculating　slew　rate　repeatedly.　Experimental　results　show　that　our　algorithm　maximizes　routing　resources　over　obstacles　and　saves　routing　resources　outside　obstacles.　Compared　with　the　conventional　OARSMT　algorithm,　our　algorithm　reduces　the　wire　length　outside　obstacles　by　as　much　as　18.74%　and　total　wire　length　by　as　much　as　6.03%.　Our　algorithm　improves　the　latest　related　algorithm　by　approximately　2%　in　terms　of　wire　length　within　a　reasonable　running　time.　Additionally,　calculating　the　slew　rate　only　accounts　for　approximately　15%　of　the　total　runing　time.　©　2016　Elsevier　B.V.　All　rights　reserved.