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Link-state routing with hop-by-hop forwarding is widely used in the Internet today. The current versions of these protocols, like OSPF, split traffic evenly over shortest paths based on link weights. However, optimizing the link weights for OSPF to the offered traffic is an NP-hard problem, and even the best setting of the weights can deviate significantly from an optimal distribution of the traffic. In this paper, we propose a new link-state routing protocol, PEFT, that splits traffic over multiple paths with an exponential penalty on longer paths. Unlike its predecessor, DEFT, our new protocol provably achieves optimal traffic engineering while retaining the simplicity of hop-by-hop forwarding. A gain of 15 % in capacity utilization over OSPF is demonstrated using the Abilene topology and traffic traces. The new protocol also leads to significant reduction in the time needed to compute the best link weights. Both the protocol and the computational methods are developed in a new conceptual framework, called network entropy maximization, which is used to identify the traffic distributions that are not only optimal but also realizable by link-state routing.