This paper proposes a novel linear formulation for the problem of segment shared protection, where the switching/merging nodes and the least-cost link-disjoint working and protection segments corresponding to each switching/merging node-pair are jointly determined for a connection request. A novel approach of arc-reversal graph transformation is introduced. We verify the ILP and compare it with three reported approaches for solving the segment shared protection problem, namely CDR, PROMISE, and OPDA, by launching dynamic connection requests on two network topologies. From the experiment results, we observe that the ILP can always yield better results in terms of the total cost taken by the working and protection segments. We conclude that the proposed ILP formulation is a step ahead of the most state-of-the-art techniques in solving the shared protection problem, which provides a means of evaluating any other segment shared protection algorithms.