In hop-by-hop networks, provision of multipath routes for all nodes can improve fault tolerance and performance. In this paper we study the multipath route calculation by constructing a directed acyclic graph (DAG) which includes all edges in the network. We define new DAG construction problems with the objectives of 1) maximizing the minimum connectivity, 2) maximizing the minimum max-flow, and 3) maximizing the minimum max-flow as an extension of shortest path routing. A family of new algorithms called Maximum Alternative Routing Algorithms (MARAs) is described, proven formally to solve the problems optimally, and contrasted with existing multipath algorithms. MARAs are evaluated for the number of paths, the length of paths, the computational complexity, and the computation time, using simulations based on several real Internet Autonomous System (AS) network topologies. We show that MARAs run in sub-second times on moderate-speed processors and achieve a significant increase in the number of paths compared to existing multipath routing algorithms. These results should help further the process of deploying multipath routing in real-world networks.