A homeless ex-convict has been arrested in the rape and torture of a Columbia University graduate student, who was held hostage for 19 hours, cut with a knife and left tied up with the bed set ablaze.

Robert Williams, 30, faces attempted murder, rape, kidnapping, arson and other charges stemming from last week's assault, police said Friday.

Investigators said evidence found at the victim's apartment and an anonymous tip pointed to Williams. The suspect, also known as William Roberts, has previous convictions for attempted murder and assault.

Williams was stopped Thursday leaving a building where a burglary had been reported. While being questioned, officers noticed he fit the description of the rape suspect, including a scar on his stomach, police said.

Williams was expected to be arraigned late Friday. It was unclear whether he had a lawyer.

The victim, who is nearing her degree at the Graduate School of Journalism, was still hospitalized with cuts to her eye lids and other injuries.

The attack shocked the journalism school and sparked fears that the rapist could strike again.

"Obviously, we're all very relieved," the school's spokeswoman, Barbara Fasciani, said about the arrest.

The attack began April 13 after the assailant slipped inside the victim's upper Manhattan apartment building and forced his way into her home. Over the next several hours, the assailant raped her on her futon bed, tied her up with computer cables, force fed her drugs and alcohol and used a knife to slit her eyelids, police said.

Before fleeing at about 4:30 p.m. Saturday, the assailant ignited a corner of the futon. The victim used the flames to loosen the cables and run for help, police said.

Investigators recovered a surveillance videotape from a neighboring market showing the man believed to be the rapist walk in wearing a large jacket over a hooded sweat shirt. He is seen walking toward an automated teller machine, where, police said, he withdrew $200 from the victim's bank account.