Center-based　clustering　has　attracted　significant　research　interest　from　both　theory　and　practice.　In　many　practical　applications,　input　data　often　contain　background　knowledge　that　can　be　used　to　improve　clustering　results.　In　this　work,　we　build　on　widely　adopted　k-center　clustering　and　model　its　input　background　knowledge　as　must-link　(ML)　and　cannot-link　(CL)　constraint　sets.　However,　most　clustering　problems　including　k-center　are　inherently　NP-hard,　while　the　more　complex　constrained　variants　are　known　to　suffer　severer　approximation　and　computation　barriers　that　significantly　limit　their　applicability.　By　employing　a　suite　of　techniques　including　reverse　dominating　sets,　linear　programming　(LP)　integral　polyhedron,　and　LP　duality,　we　arrive　at　the　first　efficient　approximation　algorithm　for　constrained　k-center　with　the　best　possible　ratio　of　2.　We　also　construct　competitive　baseline　algorithms　and　empirically　evaluate　our　approximation　algorithm　against　them　on　a　variety　of　real　datasets.　The　results　validate　our　theoretical　findings　and　demonstrate　the　great　advantages　of　our　algorithm　in　terms　of　clustering　cost,　clustering　quality,　and　running　time.　Copyright　©　2024,　Association　for　the　Advancement　of　Artificial　Intelligence　(www.aaai.org).　All　rights　reserved.