Hmm you mentioned two dogs...that might be the problem. How do the dogs get along? Are they the same sex or different sexes? Was the other dog there before the adopted greyhound arrived or did it arrive afterwards? How old are both dogs?

It could be the new dog trying to establish his place in this new pack he perceives he's joined, or trying to move up in status in that pack. Which dog seems the more dominant to you? Do either dogs act dominant to the humans in the house (pushing past you to get outside, humping you or the other dog, guarding food)?