Distributed Constraint Problem solving represents a fundamental research area in distributed artificial intelligence and multi-agent systems. The constraint density, or the ratio of the number of constraints to the number of variables, determines the difficulty of either finding a solution or minimizing the set of variable assignment conflicts. Reducing density typically reduces difficulty. We present a fully distributed technique for reducing the effective density of constraint graphs, called Virtual Structure Reduction (VSR). The VSR technique leverages the occurrence of variables that must be assigned the same value based on shared constraints and can improve solver performance using existing algorithms. We discuss our Distributed Constraint Optimization Problem (DCOP) solver, integrated with the Distributed Stochastic Algorithm (DSA), called VSR-DSA. The VSR-DSA algorithm demonstrates performance gains vs DSA in both solution quality and time on 3-coloring problems.