Wash radishes and green tops thoroughly. Cut radishes into thin slices to equal 1/2 cup; chop radish tops to equal 1/3 cup.
Cook pasta according to package directions, omitting salt and fat; keep warm.
Heat oil in a large nonstick skillet over medium-high heat. Add radishes, radish tops, and garlic; sauté 5 minutes, stirring frequently. Add potatoes and broth; bring to a boil. Cover, reduce heat, and simmer 7 minutes or until potatoes are tender. Add asparagus; cook 3 minutes. Add salt. Combine potato mixture and pasta; toss well. Sprinkle with cheese.