Packet Routing on the Grid

The packet routing problem, i.e., the problem to send a given set of unit-size packets through a network on time, belongs to one of the most fundamental routing problems with important practical applications, e.g., in traffic routing, parallel computing, and the design of communication protocols. The problem involves critical routing and scheduling decisions. One has to determine a suitable (short) origindestination path for each packet and resolve occurring conflicts between packets whose paths have an edge in common. The overall aim is to find a path for each packet and a routing schedule with minimum makespan. A significant topology for practical applications are grid graphs. In this paper, we therefore investigate the packet routing problem under the restriction that the underlying graph is a grid. We establish approximation algorithms and complexity results for the general problem on grids, and under various constraints on the start and destination vertices or on the paths of the packets.