A suite of parallel algorithms for ordering DNA sequences (termed PARODS) is presented. The algorithms in PARODS are based on an earlier serial algorithm, ODS, which is a physical mapping algorithm based on simulated annealing. Parallel algorithms for simulated annealing based on Markov chain decomposition are proposed and applied to the problem of physical mapping. Perturbation methods and problem-specific annealing heuristics are proposed and described. Implementations of parallel Single Instruction Multiple Data (SIMD) algorithms on a 2048 processor MasPar MP-2 system and implementations of parallel Multiple Instruction Multiple Data (MIMD) algorithms on an 8 processor Intel iPSC/860 system are presented. The convergence, speedup and scalability characteristics of the aforementioned algorithms are analyzed and discussed. The best SIMD algorithm is shown to have a speedup of approximately 1000 on the 2048 processor MasPar MP-2 system, whereas the best MIMD algorithm is shown to have a speedup of approximately 5 on the 8 processor Intel iPSC/860 system.