Possibly the most common folkloric explanation offered is that they are thrown over to indicate the territory of drug gang. In this theory, particular brands or colour of trainer mark out particular gangs. They are high up so they are easily seen and identified, but not easily removed - thus ensuring that the message is clear to rival gangs.
Another explanation is also drug related. In this version, however, the shoes are said to be put in place when a new supply of drugs is in the area. On seeing new trainers, local drug takers know that supplies are ready and can head for the local supplier.
Of course, neither of these two explanations bear much scrutiny. If true, they are extraordinarily inefficient compared to either old methods - such as graffiti - or modern methods such as text messages. They are also prone to logistical difficulties and the chance of either the shoes being removed (hence ending their use as a marker of any kind) or remaining in place (hence being useless as a timely notification).
A alternative view is that the practice is related somehow to the use of amulets to dispel evil. As in the case of witch-bottles, the placing of personal items at boundaries is said to ward off evil spirits. Could hurling one's trainers over a wire perform a similar function - perhaps for a whole street?
Simpler, less esoteric explanations abound: simple larkishness or a form of bullying. Whatever the reason for this minor but persistent practice, it continues to persist as a small reminder that not all human activities belong to the sphere of the rational.