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An automated path planning algorithm for a mobile robot in a structured environment is presented. An algorithm based on the Quine-McCluskey method of finding prime implicants in a logical expression is used to isolate all the largest rectangular free convex areas in a specified environment. The free convex areas are represented as nodes in a graph, and a graph traversal strategy that dynamically allocates costs to graph paths is used. Complexity of the algorithm and a strategy to trade optimality for smaller computation time are discussed.