San Francisco police are searching for more suspects in the three-day-long torture of a homeless man who was beaten to death and dumped in a pond in Golden Gate Park, a brutal crime targeting a vulnerable population that has become a major flashpoint in this city and others with rising housing costs.

Homelessness is a major blight in San Francisco, which is famous for new condos, cutting-edge dining and jaw-dropping home prices fueled in recent years by a rapid rise in technology-based jobs. But with thousands of wealthier people moving in, complaints have cropped up about the overwhelming visibility of people who live on the streets.

Earlier this year, a founder of a technology startup posted an open letter to San Francisco Mayor Ed Lee complaining that he "shouldn't have to see the pain, struggle, and despair of homeless people" on his way to work.

Homelessness is an issue facing other expensive cities, such as Seattle and Los Angeles.

Two transients were charged this week in the slaying of Stephen Williams, 66, who was brutally beaten over three days before he was knocked unconscious and his body dumped into Alvord Lake near Haight Street, a popular hangout for young transients. They had no connections to the victim, and a motive is under investigation. Police searched Wednesday for more suspects.

San Francisco cleared out several sidewalk tent encampments earlier this year, citing threats to public health and safety. Elected officials are debating the best way to house people who lack permanent places to live.

The efforts come after three young transients were arrested last year in the deaths of a popular yoga teacher and a Canadian backpacker, whose body also was found in Golden Gate Park.

Both Seattle and Los Angeles have declared crises over the number of people living on the streets, pledging millions of dollars for housing and social services. The fast-growing city in Washington state also has seen recent attacks: Three homeless boys were charged in February with killing two people at a longstanding encampment.

In the San Francisco killing, the assault started on May 22 when Nikki Lee Williams, 36, known as "Evil," forced the victim into a pond with help from other people and repeatedly struck Stephen Williams and held his head underwater, according to court documents. Nikki Williams and the victim are not related.

The following day, 19-year-old Stephen Billingsley, known as "Pizza Steve," repeatedly struck and stomped Stephen Williams along Haight Street until the man lost consciousness. The day after that, Williams, Billingsley and others again brutally assaulted Stephen Williams, leaving him unconscious near Alvord Lake.

Billingsley then dragged him to the pond, where a park gardener found his body hours later, court records show. The medical examiner says Stephen Williams died from "multiple traumatic injuries."

The suspects found Williams each day over the three days because they all live in the same area and visit the same places, San Francisco Officer Carlos Manfredi said. Police are looking for additional suspects involved in the attack.

Billingsley is charged with murder, torture, conspiracy, elder abuse and assault. Nikki Williams is charged with conspiracy, assault, elder abuse and false imprisonment. They have pleaded not guilty and are in jail, with bail set at $1 million each.

The public defender assigned to Williams declined to comment through an office spokeswoman. It's unclear if Billingsley has retained an attorney. The Bar Association of San Francisco said it has not received a request to represent him.

The suspects are "transients without longstanding ties" to San Francisco and have no prior arrest history in the city, Manfredi said.