Alpern, Steve; Gal, Shmuel (2003), "Chapter 8. Search on the Infinite Line", The Theory of Search Games and Rendezvous, Part 2, International Series in Operations Research & Management Science, vol. 55, pp. 123–144, doi:10.1007/0-306-48212-6_8. On p. 124, Alpern and Gal write "no algorithm for solving the problem for a general probability distribution function has been found during about 37 years since the LSP was first presented."
Alpern, Steve; Gal, Shmuel (2003), "Section 8.7. A Dynamic Programming Algorithm for the LSP", The Theory of Search Games and Rendezvous, Part 2, International Series in Operations Research & Management Science, vol. 55, pp. 139–144, doi:10.1007/0-306-48212-6_8