Delay Constrained Subtree Homeomorphism Problem with Applications

Virtual world and other collaborative applications are increasingly becoming popular among Internet users. In such applications, users interact with each other through digital entities or avatars. In order to preserve the user experience, it is important that certain Quality of Service (QoS) requirements (e.g., delay and bandwidth) are satisfied by the interactions. These QoS requirements are usually defined by the application designer. When applications with such QoS requirements are being deployed on a network of servers, an appropriate set of servers capable of satisfying the QoS constraints of the interactions must be identified. This identification process is nothing, but the subgraph homeomorphism problem. In this paper, we present polynomial-time solutions for a special case of this problem viz. subtree homeomorphism problem, wherein the guest and the host graphs are both trees. We also discuss generalizations of the subtree homeomorphism problem and present polynomial-time solutions.