Many　practical　applications　impose　a　new　challenge　of　utilizing　instance-level　background　knowledge　(e.g.,　subsets　of　similar　or　dissimilar　data　points)　within　their　input　data　to　improve　clustering　results.　In　this　work,　we　build　on　the　widely　adopted　k-center　clustering,　modeling　its　input　instance-level　background　knowledge　as　must-link　(ML)　and　cannot-link　(CL)　constraint　sets,　and　formulate　the　constrained　k-center　problem.　Given　the　long-standing　challenge　of　developing　efficient　algorithms　for　constrained　clustering　problems,　we　first　derive　an　efficient　approximation　algorithm　for　constrained　k-center　at　the　best　possible　approximation　ratio　of　2　with　linear　programming　(LP)-rounding　technology.　Recognizing　the　limitations　of　LP-rounding　algorithms　including　high　runtime　complexity　and　challenges　in　parallelization,　we　subsequently　develop　a　greedy　algorithm　that　does　not　rely　on　the　LP　and　can　be　efficiently　parallelized.　This　algorithm　also　achieves　the　same　approximation　ratio　2　but　with　lower　runtime　complexity.　Lastly,　we　empirically　evaluate　our　approximation　algorithm　against　baselines　on　various　real　datasets,　validating　our　theoretical　findings　and　demonstrating　significant　advantages　of　our　algorithm　in　terms　of　clustering　cost,　quality,　and　runtime　complexity.