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A fast and efficient method for finding all dc solutions of resistive piecewise linear (PWL) circuits is proposed. This method is based on the introduction of suitable polyhedra, denoted as oversized, surrounding a sequence of certain portions of PWL characteristics. Unlike the minimum-sized polyhedra introduced in the standard polyhedral method, these oversized polyhedra are characterized by simple polygons (for example, triangles) with a low number of vertices. The overall algorithm is so structured according to a sequence of binary trees, composed of nodes connected by oriented arcs, and it is based on a linear programming test characterized by low-dimension tableaux. The advantages of using polyhedra with a few number of vertices are double: There are minor numerical errors in tableau solutions, and the total CPU time decreases remarkably. Therefore, it is possible to deal with higher rank circuits in comparison with the standard polyhedral method.