Answer: Weeds have many local names, making it difficult to know for sure which one you are talking about. Two which grow in your area and which are aggressive invaders are Virginia Buttonweed and Nutgrass (or more accurately Nutsedge).
Virginia Buttonweed is a vining, low growing weed with straplike leaves about an inch long and four-petaled white flowers about 1/4 inch in diameter. Your control options are diligent hand pulling (never let it up for air!) and herbicide sprays. Roundup will control it with more than one application, but take care not to let spray drift onto desirable plants or you will control them too!
Nutgrass is a triangular-stemmed upright growing sedge which has long thin leaves and sets small 3/8" tubers underground. Controls for nutgrass in a flower bed are the same as for Virginia Buttonweed.
Once you have vanquished the weeds, install some sort of edging around the bed, and mulch any exposed soil to prevent reinfestation. Good luck!
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