Ordering clones from a genomic library into physical maps of whole chromosomes presents a central computational problem in genetics. Chromosome reconstruction via clone ordering is usually isomorphic to the NP-complete Optimal Linear Arrangement problem. Parallel SIMD and MIMD algorithms for simulated annealing based on Markov chain distribution are proposed and applied to the problem of chromosome reconstruction via clone ordering. Perturbation methods and problem-specific annealing heuristics are proposed and described. The SIMD algorithms are implemented on a 2048 processor MasPar MP-2 system which is an SIMD 2-D toroidal mesh architecture whereas the MIMD algorithms are implemented on an 8 processor Intel iPSC/860 which is an MIMD hypercube architecture. A comparative analysis of the various SIMD and MIMD algorithms is presented in which the convergence, speedup, and scalability characteristics of the various algorithms are analyzed and discussed. On a fine-grained, massively parallel SIMD architecture with a low synchronization overhead such as the MasPar MP-2, a parallel simulated annealing algorithm based on multiple periodically interacting searches performs the best. For a coarse-grained MIMD architecture with high synchronization overhead such as the Intel iPSC/860, a parallel simulated annealing algorithm based on multiple independent searches yields the best results. In either case, distribution of clonal data across multiple processors is shown to exacerbate the tendency of the parallel simulated annealing algorithm to get trapped in a local optimum.