Since when is it okay to let your dog out to take a dump in your neighbors front yard?

I live in a nice cul-de-sac walking distance from a lake. I love my nice and peaceful neighborhood, you rarely see neighbors but EVERYDAY I do see huge crap on my front lawn and I'm pretty disgusted about it! I've seen three dogs with tags roaming around by themselves (of course) taking dumps where ever they please! One time one of them ripped open a full trash bag I left out for the trash company to pick up and had to pick up the trash with my hands! Am I expecting too much from my neighbors, I mean this is a nice upscale neighborhood! I have a dog myself but he does his business in OUR backyard and I clean it up! I'm just getting tired of having to watch where I step when I get my mail! What can I do about this being that I have no clue who the owners are? Please help!