Capacity Provisioning a Valiant Load-Balanced Network

Valiant load balancing (VLB), also called two-stage load balancing, is gaining popularity as a routing scheme that can serve arbitrary traffic matrices. To date, VLB network design is well understood on a logical full-mesh topology, where VLB is optimal even when nodes can fail. In this paper, we address the design and capacity provisioning of arbitrary VLB network topologies. First, we introduce an algorithm to determine if VLB can serve all traffic matrices when a fixed number of arbitrary links fail, and we show how to find a min-cost expansion of the network - via link upgrades and installs - so that it is resilient to these failures. Additionally, we propose a method to design a new VLB network under the fixed-charge network design cost model. Finally, we prove that VLB is no longer optimal on unrestricted topologies, and can require more capacity than shortest path routing to serve all traffic matrices on some topologies. These results rely on a novel theorem that characterizes the capacity VLB requires of links crossing each cut, i.e., a partition, of the network´s nodes.