Abolish all zoning laws and other restrictions on housing size, density, and usage. Also get rid of rent control (since developers have little incentive to build affordable units when existing ones are already rent-controlled). That should go a long way toward promoting affordable housing.
Why is homelessness less of a problem in Europe despite their real estate development regulation being quite strict?
Is it actually stricter than in the US? Even is it is (which I'm skeptical of), American-style anti-density zoning is basically designed to prevent low-income development.
Exclusionary zoning is a predominately American phenomenon.
A good deal of homelessness is the result of factors affordable housing can't fix (drug addiction, mental illness, etc):
Houston is more affordable than most major US cities though:
