Subnet generation problem: A new network routing problem

Abstract

We introduce a new type of network routing problem, the subnet generation problem (SGP) which is a special case of the traffic placement problem (TPP). In the TPP, given (1) a network which consists of routers and links, and (2) a set of point-to-point traffic demands to be placed including finding feasible routes, the objective is to minimize the sum of costs of the unplaced demands subject to the Quality-of-Service routing constraints. The SGP is a TPP with an extra set of constraints that restricts the combinations of demands to be placed. In our SGP, each router has a fixed amount of information-gain that is to be transmitted to every other router in the subnet. A subnet is defined as any subset of the routers in the network. This means that every router in the subnet will have exactly the same total information-gain. The objective is to find a subnet that maximizes the total information-gain: there must be a demand with a valid path between every pair of routers in the subnet. The reason for creating demands among the routers arises from the fact that every node in a selected group of routers is required to be a client and a server. The figure below shows an example of a subnet and a path solution. We describe a structure to split the problem into a master problem (select a set of demands to be placed) and a subproblem (compute a feasible set of paths for the demands selected by the master problem). To solve the SGP, we first apply a state-of-art hybrid tree search algorithm1, designed to solve the TPP. Then, we explore how the subnet structure in the SGP could be used to solve the problem more efficiently. In particular, we focus on balancing search between the master problem and the subproblem to maximize the solution quality within a fixed computational time. © Springer-Verlag Berlin Heidelberg 2005.