In many networks, it is less costly to transmit a packet to any node in a set of neighbors than to one specific neighbor. This observation was previously exploited by opportunistic routing protocols by using single-path routing metrics to assign to each node a group of candidate relays for a particular destination. This paper addresses the least-cost anypath routing (LCAR) problem: how to assign a set of candidate relays at each node for a given destination such that the expected cost of forwarding a packet to the destination is minimized. The key is the following tradeoff: On one hand, increasing the number of candidate relays decreases the forwarding cost, but on the other, it increases the likelihood of "veering" away from the shortest-path route. Prior proposals based on single-path routing metrics or geographic coordinates do not explicitly consider this tradeoff and, as a result, do not always make optimal choices. The LCAR algorithm and its framework are general and can be applied to a variety of networks and cost models. We show how LCAR can incorporate different aspects of underlying coordination protocols, for example a link-layer protocol that randomly selects which receiving node will forward a packet, or the possibility that multiple nodes mistakenly forward a packet. In either case, the LCAR algorithm finds the optimal choice of candidate relays that takes into account these properties of the link layer. Finally, we apply LCAR to low-power, low-rate wireless communication and introduce a new wireless link-layer technique to decrease energy transmission costs in conjunction with anypath routing. Simulations show significant reductions in transmission cost to opportunistic routing using single-path metrics. Furthermore, LCAR routes are more robust and stable than those based on single-path distances due to the integrative nature of the LCAR's route cost metric.
