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Constrained discrete optimization problems are encountered in many areas of communication and machine learning. We consider the case where the objective function satisfies Bellman&#x0027;s optimality principle without the constraints on which we place no conditions. We first show that these problems are a generalization of optimization in constrained Markov decision processes with finite horizon used in reinforcement learning and are NP-Hard. We then present a novel multi-survivor dynamic programming (msDP) algorithm that guarantees optimality at significant computational savings. We demonstrate this by solving 5G quantizer bit allocation and DNA fragment assembly problems. The results are very promising and suggest that msDP can be used for many applications.

A Low-Complexity Multi-Survivor Dynamic Programming for Constrained Discrete Optimization