In a large bowl combine melon, water, fructose, and ginger. Place melon mixture, a portion at a time, in a food processor bowl or blender container. Cover and proces or blend until smooth.
Pour melon mixture into a 13x9x2-inch baking pan; cover with foil. Freeze about 4 hours or until almost firm. Break the mixture into small chunks; transfer to a chilled, large bowl. Beat with an electric mixer until slushy. Return mixture to pan. Cover; freeze at least 4 hours more.
Before serving, let stand at room temperature about 5 minutes. Makes sixteen 1/2-cup servings.