Let　G　=　(V,　E)　be　a　given　graph,　S　subset　of　V　be　a　terminal　set,　r　is　an　element　of　S　be　the　selected　root.　Assume　that　c　:　E　-＞　R+　and　d　:　E　-＞　R+　are　cost　and　delay　functions　on　the　edges　respectively.　The　shallow-light　Steiner　tree　(SLST)　problem　is　to　compute　a　minimum　cost　tree　spanning　all　the　terminals　of　5,　such　that　the　delay　between　r　and　every　other　terminal　is　bounded　by　a　given　delay　constraint　D　is　an　element　of　R-0(+).　Since　in　real　network,　the　cost　and　delay　of　a　link　are　always　related,　this　paper　addresses　two　such　special　cases:　the　constrained　Steiner　tree　(CST)　problem,　a　special　case　of　the　SLST　problem　that　c(e)　=　sigma　d(e)　for　every　edge,　and　the　constrained　spanning　tree　(CPT)　problem,　a　further　special　case　of　the　CST　problem　when　S　=　V.　This　paper　first　shows　that　even　when　c(e)　=　d(c),　the　CPT　problem　is　NP-hard,　and　admits　no　(1　+　epsilon,　gamma　ln　(vertical　bar　V　vertical　bar)　approximation　algorithm　algorithm　for　some　fixed　gamma　＞　0　and　any　epsilon　＜　1/vertical　bar　V　vertical　bar+vertical　bar　E　vertical　bar+1　The　inapproximability　result　can　be　applied　to　the　CST　problem　immediately.　Based　on　the　above　observation　of　the　hardness　to　develop　a　single　factor　approximation　algorithm,　we　give　an　approximation　algorithm　with　a　bifactor　ratio　of　(rho,　1.39　+　2.78/rho　-　1)　for　the　CST　problem,　where　1.39　is　the　best　approximation　ratio　for　the　minimum　Steiner　tree　problem　in　the　current　state　of　the　art.　As　a　consequence,　for　the　applications　where　cost　and　delay　are　of　equal　importance,　an　approximation　with　bifactor　(2.87,　2.87)　for　CST　can　be　immediately　obtained　by　setting　rho　=　1.39　+　2.78/rho　-　1.　This　indicates　that　the　SLST　problem　admits　approximation　algorithms　with　constant　bifactor　ratio,　when　the　cost　and　delay　are　linearly　dependent.