Fiber-Wireless (FiWi) networks have received considerable attention in the research community in the last few years as they offer an attractive way of integrating optical and wireless technology. As in every other type of networks, routing plays a major role in FiWi networks. Accordingly, a number of routing algorithms for FiWi networks have been proposed. Most of the routing algorithms attempt to find the "shortest path" from the source to the destination. A recent paper proposed a novel path length metric, where the contribution of a link towards path length computation depends not only on that link but also every other link that constitutes the path from the source to the destination. In this paper we address the problem of computing the shortest path using this path length metric. Moreover, we consider a variation of the metric and also provide an algorithm to compute the shortest path using this variation. As multipath routing provides a number of advantages over single path routing, we consider disjoint path routing with the new path length metric. We show that while the single path computation problem can be solved in polynomial time in both the cases, the disjoint path computation problem is NP-complete. We provide optimal solution for the NP-complete problem using integer linear programming and also provide two approximation algorithms with a performance bound of 4 and 2 respectively. The experimental evaluation of the approximation algorithms produced a near optimal solution in a fraction of a second.