This is a Saluki, a hunting dog originally bred by nomadic desert tribes in the Arabian Peninsula to hunt gazelle. Salukis are sighthounds which means the hunt using their sight and speed as opposed to scent and stamina. That said, Salukis are considered to be the fastest long-distance running dogs in the world. Greyhounds, an obviously similar breed, can hit 45 mph up to around 2,600 feet while Saulkis have been clocked at 42.8 mph for longer periods.
According to Wikipedia, "While hunting hares, Bedouin hunters would sometimes ride close to their quarry on a camel holding such a dog, which would be thrown towards the prey while at speed to give the dog a running start. Gazelle hunters have also used hawks or falcons to attack the head of the prey so that the dogs could then bring down the distracted animal."