It is suspected that the alleged killer, Ichihashi Tatsuya, had his eye on Hawker for a period of time before actually approaching her. Partly fueled by interviews with local residents, the theory goes that he had been stalking her. It is speculated that he knew where she lived, worked, and socialized with her friends.
Update 8: [Monday April 2nd] Over the weekend Lucie Blackman's father spoke out in support of the Hawker family.
Articles being carried by both the Japan Times and the Mainichi (English) hint at growing impatience with the pace of the investigation. Mr. Bill Hawker demonstrated impressive restraint and diplomacy during the first news conference last Wednesday when he said that he was satisfied with the investigation being carried out by police (a diplomatic tact was likely coached by members of the British embassy). Now he is attempting to apply some pressure by saying that the country has been "shamed" by this crime.