Packet broadcasting mechanism for mesh interconnected multi-computers

A system is provided for packet broadcasting in a mesh-interconnected multi-computer network having a plurality of routers. The system includes a plurality of arbiters, interconnected to each of the plurality of routers, configured to live-lock free arbiter between the two or more packet broadcast requests using a shared priority matrix, implemented by a binary matrix, that selects one of the two or more packet broadcast requests and includes a column for each of the plurality of routers. The shared priority matrix is shared amongst the plurality of arbiters and stores priority information determined from summing the matrix column values and relating to a correspondence between a plurality of packet broadcast requests, including the two or more packet broadcast requests, with respect to priorities assigned to each of the plurality of packet broadcast requests. Each of columns of the shared priority matrix corresponds to a respective one of the routers.