Public housing is typically a sink hole for taxpayer money - costly to build and poorly maintained.  As well, large public housing projects are often crime ridden because the landlord (i.e. government) is unwilling or unable to evict the criminals.   We should instead try rent subsidies so that the homeless can afford to rent from  private sector landlords who  maintain their properties to a much higher standard than governments do.  An added bonus to the rent subsidy approach is that recipients have a much wider choice of where they live and don't have to be confined to public housing ghettos.