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We propose two cross-diamond-hexagonal search (CDHS) algorithms, which differ from each other by their sizes of hexagonal search patterns. These algorithms basically employ two cross-shaped search patterns consecutively in the very beginning steps and switch using diamond-shaped patterns. To further reduce the checking points, two pairs of hexagonal search patterns are proposed in conjunction with candidates found located at diamond corners. Experimental results show that the proposed CDHSs perform faster than the diamond search (DS) by about 144% and the cross-diamond search (CDS) by about 73%, whereas similar prediction quality is still maintained.