Solving a system of linear equations has been widely used to compute seeds for LFSR reseeding to compress test patterns. However, as chip size is growing, solving linear equations requires a large number of computations that is proportional to n3. This paper proposes a new scan chain architecture and algorithm so that the order of computation is proportional to the number of scan cells in a chip. The new architecture is a methodology change that does not require complex design-for-testability (DFT) as proposed in the previous techniques. Instead of solving linear equations, the proposed new seed computation algorithm topologically determines seeds for test vectors. The compression ratio might be slightly lower than the other approaches, but the proposed approach can handle larger designs in a reasonable amount of time. Computation analysis shows that, for 1 million scan cell design, if we assume it takes 1 msec for the proposed technique to compute seeds, it would take more than 14 minutes for other techniques that solve linear equations.