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 shown to be isomorphic to the NP-completeOptimal Linear Orderingproblem. Massively parallel 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 arc proposed and described. These algorithms are implemented on a 2048 processor MasPar MP-2 system which is an SIMD 2-D toroidal mesh architecture. Convergence, speedup and scalability characteristics of the various algorithms are analyzed and discussed. Results indicate that for an optimal clone ordering, a single Markov chain of solution states should not be distributed across more than two adjoining processing elements (PE's) on the MasPar MP-2.