Among metropolitan areas in the South, the nation’s fastest-growing region, Columbia is late to a boom period.

New Orleans rebounded after Hurricane Katrina and became a hub for start-up companies. Raleigh, N.C., has logged significant job gains. Greenville, S.C., transformed its downtown, earning the admiration of Columbia. And in Nashville, an investment company recently introduced an exchange-traded fund exclusively featuring area businesses.

In Columbia, which has branded itself “the new Southern hot spot,” residents say the city’s time has come.

They point to plans for the 181-acre campus that once housed the state’s mental hospital and will, over the next two decades, become a mixed-use development with an annual economic impact of more than $1 billion. Speculation is rampant that a minor-league baseball team will relocate to Columbia. Less flashy projects also abound, including the conversion of a vacant office building into housing for University of South Carolina students, some of the more than 780,000 people who live in the metropolitan area.

But business owners are warning that rising homelessness in Richland County — up 43 percent in two years, according to the South Carolina Coalition for the Homeless, an increase many blame on an absence of affordable housing options and a sluggish national economy — is imperiling the area’s prospects.