Explain from these scenarios whether or not a warrant is appropriate for an arrest, and why?

Search Warrant:

Gary Ridgway was known to have been a frequent customer to well known prostitution strips and streets around Seattle, near the SEATAC Airport, and Tacoma. After King County Sheriff's Office put together a task force to find the Green River Killer, they put more officers on the street to try and find potential suspects picking up women. Gary, was arrested in 1982 and 2001 on prostitution charges, and from there became a suspect in the Green River case. Despite having a truck that matched witness statements of the killer's truck, and undergoing interviews and polygraph tests, Ridgway was released since there was no outside evidence and he passed the poly. Even though he passed, police collected DNA samples from him to keep in case of further involvement. At the time of this case, DNA profiling and matching were not prevelent enough, nor were they reliable in court because of the lack of research done using DNA matches. Years later though, suspects were found with microscopic paint spray and carpet particles on their body. Gary Ridgway worked at a paint manufacturing company. Police used this evidence as a way to get a search warrent of Gary Ridgway's house and Gary Ridgway's truck. The warrant was specified to get samples of the house carpet and the truck flooring, to see if there was a match in the particles to the paint and carpet particles found on the victims.

Arrest Warrant:

After the search warrant discovered an exact match in the paint particles and carpet particles found in RIdway's truck, to those found on the Victim's bodies, Ridgway's DNA was then compared to the DNA evidence (semen) found within other victims. The DNA evidence, while not deemed 100% accurate at the time, found Gary's DNA to be an exact match. With the DNA match and the particle match, the Sheriff's department got an arrest warrant for Ridgway, and arrived at his work and took him into custody.