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In this work we propose a heuristic clearing method of day-ahead electricity markets. In the first part of the process, a computationally less demanding problem is solved using an approximation of the cumulative demand and supply curves, which are derived via the aggregation of simple bids. Based on the outcome of this problem, estimated ranges for the clearing prices of individual periods are determined. In the final step, the clearing for the original bid set is solved, taking into account the price ranges determined previously as constraints. Adding such constraints reduces the feasibility region of the clearing problem. By removing simple bids whose acceptance or rejection is already determined by the assumed price range constraints, the size of the problem is also significantly reduced. Via simple examples, we show that due to the possible paradox rejection of block bids the proposed bid-aggregation based approach may result in a suboptimal solution or in an infeasible problem, but we also point out that these pitfalls of the algorithm may be avoided by using different aggregation patterns. We propose to construct multiple different aggregation patterns and to use parallel computing to enhance the performance of the algorithm. We test the proposed approach on setups of various problem sizes, and conclude that in the case of parallel computing with 4 threads a high success rate and a significant gain in computational speed may be achieved.