I have read that Albanians have a Caucasian connection, being descended from the Caucasus. There have been heated debates on anthropology boards, but a simple view of genetics studies indicate that Albanians are not descended from the Caucasus. Albanian males have a high degree of southeastern European haplogroup E3b and a low degree of haplogroup J2-M67, which is high in the Caucasus. Albanian males also have a relatively high amount of haplogroup I1b, which is from the Balkans, and may be low in the Caucasus.
It is unknown to what degree Greeks are descended from speakers of Albanian, and vice versa. Because many Greek- and Albanian males are haplogroup E3b, it's almost irrelevant. Haplogroup I1b in Greece is interesting, as it may indicate an Albanian or Vlach connection. One thing that is interesting in Albanians and Greeks (and other Balkan peoples) is that there is an inverse relationship between haplogroups I1b and R1a1 when compared to northern Slavs. Russians, Poles and Ukrainians have higher R1a1 and lower I1b, and Balkan peoples have higher I1b and lower R1a1 (even in Greece).
I looked at a study done by Semino et al., which looked at haplogroups J and E in Europe, to get info on Caucasians. Other than that, I don't know if there is much info on Caucasian DNA. I have seen other DNA studies which show that Albanian males are in large part descended from the Balkans.