Resource allocation in cube network systems based on the covering radius

When multiple copies of a certain resource exist in a cube network system, it is desirable that every nonresource node can reach the resource in a given number of hops. In this paper, we introduce systematic approaches to resource allocation in a cube system so that each nonresource node is connected with a specified number of resource copies and that the allocation performance measure of interest is optimized. The methodology used is based on the covering radius results of known codes. These codes aid in constructing desired linear codes whose codewords address nodes where resource copies are placed. The resource allocation problem is translated to an integer nonlinear program whose best possible solution can be identified quickly by taking advantage of basic properties derived from the known codes, yielding an optimal or near-optimal allocation result. Those basic properties lead to drastic time complexity reduction (up to several orders of magnitude smaller), in particular for large system sizes. Our approaches are applicable to any cube size, often arriving at more efficient allocation outcomes than what are attainable using prior schemes