In　recent　years,　Data　Center　Network　(DCN)　has　become　a　promising　and　efficient　data　processing　infrastructure　for　cloud　computing.　One　important　mission　of　DCN　is　to　serve　the　ever-growing　demand　for　computation,　storage,　and　networking　for　multiple　tenants　in　cloud　computing.　This　paper　uses　the　notion　of　elasticity　to　measure　the　potential　growth　of　multiple　tenants　in　terms　of　both　computation　and　communication　resources.　Our　objective　is　to　maximize　the　elasticity　for　DCNs.　We　consider　the　multiple　virtual　cluster　placement　problem　with　the　hose　model　under　the　computation　and　communication　constraints.　We　first　formulate　this　problem　as　an　Integer　Linear　Programming　(ILP)　problem.　Unfortunately,　the　formulated　ILP　problem　cannot　be　solved　by　the　simplex　or　eclipse　methods　because　of　a　large　number　of　variables　and　constraints.　Therefore,　we　propose　an　efficient　scheme　based　on　the　Dynamic　Programming　(DP)　and　analyze　its　optimality　and　complexity.　Furthermore,　we　propose　a　heuristic　algorithm　for　placement　that　maximizes　the　elasticity　and　guarantees　the　bandwidth　demand　as　well　as　lower　complexity.　Extensive　evaluations　demonstrate　that　our　schemes　outperform　existing　state-of-the-art　methods　in　terms　of　both　elasticity　and　efficiency.　©　2019　IEEE.