In the design of algorithms, the greedy paradigm provides a powerful tool for solving efficiently classical computational problems, within the framework of procedural languages. However, expressing these algorithms within the declarative framework of logic-based languages has proven a difficult research challenge. In this paper, we extend the framework of Datalog-like languages to obtain simple declarative formulations for such problems, and propose effective implementation techniques to ensure computational complexities comparable to those of procedural formulations. These advances are achieved through the use of the choice construct, extended with preference annotations to effect the selection of alternative stable-models and nondeterministic fixpoints. We show that, with suitable storage structures, the differential fixpoint computation of our programs matches the complexity of procedural algorithms in classical search and optimization problems.