Do you need an arrest warrant issued against a serial killer before a police officer is authorized to arrest him? Is the arrest warrant issued by the court? The head of RHD (LAPD) cannot issue an arrest warrant, now, can he? How long does it take for the court to issue an arrest warrant upon request?
FYI, it doesn't matter whether he's a serial killer or a serial shoplifter; the rules are the same. Generally speaking, an arrest warrant is only
needed when the arrest is (1) to take place in the suspect's home AND (2) is under non-emergency conditions. The only point of condition (2) is just to clarify that although normally the police need a warrant to arrest someone in their home, they can arrest a person in his home without a warrant if it's an emergency--for example, if the police are called over on a domestic violence 911 call and there's a good reason to arrest him then and there, such as that his victim is still in danger so they need to get him away from her right away. (So in this sense only, it might matter whether he's a serial killer or a serial shoplifter: a serial killer is probably more likely to create an emergency situation, e.g. by taking a hostage, than a serial shoplifter, so a serial killer is MORE likely to be arrestable without a warrant.)
However, although the cops usually don't
need an arrest warrant because they usually arrest people someplace other than in their homes, an arrest warrant may
exist for other reasons (e.g., if the suspect can't be found, an arrest warrant might be issued just so that if a cop does happen to find the guy--say he gets pulled over for a traffic stop in another state--the cop's quickie background check will tell him he should NOT let the guy go with a ticket, but instead bring him in).
So the general rule is, the cops can get an arrest warrant if they have probable cause to believe the guy committed a crime, but they don't actually NEED one unless they're going to arrest him at his home, and even in that case, if it's an emergency they don't need a warrant. Or, to put it another way:
(1) If the police have probable cause to believe the guy committed a crime, they can either get a warrant or just go arrest him without needing a warrant,
(2)...unless they plan to arrest him at his home, in which case they need a warrant...
(3) ...except if it's an emergency, in which case they can arrest him at his home without a warrant; and
(4) Even when the police don't technically need a warrant, they might still ask for one to be issued by a judge if it would be helpful, such as if the suspect can't be found and they just want to flag his record with an arrest warrant so that if he has any minor run-ins with the law, those cops will know to detain him instead of letting him go.