Host-Bypass: Approximating Node-weighted Connectivity Problems In Two-Tier Networks

We focus on network design problems in those networks which have two distinct sets or tiers of network nodes: hosts and infrastructure nodes. For instance, wireless mesh networks are often composed of the infrastructure nodes which relay the data between the client nodes. Similarly, the switches (infrastructure) in data center networks sit between the servers (hosts) to route the information flow. In such two-tier networks, a network designer typically requires paths between hosts in the host-tier through nodes in the infrastructure-tier while minimizing the cost in building the network. A subtle constraint, which we call as the host-tier constraint, in choosing such paths requires that no host in host-tier is an intermediate node on any path. Often, this constraint is necessary for designing network topologies in practice. In this work, we first show that the network design algorithms in prior work are inapplicable to the above described Two-Tier Network Connectivity (TTNC) problem with the host-tier constraint. We then investigate TTNC problem with the goal of minimizing the cost in building the network. We show that TTNC problem is NP-hard, and present Host-Bypass, the first algorithm for TTNC problem with provable performance bound on cost of O(h 1 2 logh) where h is the number of host nodes, ǫ > 0. Host-Bypass has polynomial running time of O(n 1 ǫ h 2 ǫ ) (n is total number of nodes), and our simulation study shows that Host-Bypass performs close to optimal and is 30% better than a heuristic from an algorithm in prior work.