Any finite combinatorial problem with a known logical circuit can be encoded as a tensor network whose contraction defines an explicit, though generally inefficient, solution equation.
A survey on combinatorial optimization
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abstract
This survey revisits classical combinatorial optimization algorithms and extends them to two-stage stochastic models, particularly focusing on client-element problems. We reformulate these problems to optimize element selection under uncertainty and present two key sampling algorithms: SSA and Boost-and-Sample, highlighting their performance guarantees. Additionally, we explore correlation-robust optimization, introducing the concept of the correlation gap, which enables approximations using independent distributions with minimal accuracy loss. This survey analyzes and presents foundational combinatorial optimization methods for researchers at the intersection of this field and reinforcement learning.
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Explicit Solution Equation for Every Combinatorial Problem via Tensor Networks: MeLoCoToN
Any finite combinatorial problem with a known logical circuit can be encoded as a tensor network whose contraction defines an explicit, though generally inefficient, solution equation.