Illustration of data insertion in JC. All jump-points are marked as bold blue lines, and all cut-points are marked as bold black lines. The points that satisfy the jump-condition or the cut-condition but reside in the jumped (purple) area are marked with blue and black dotted lines, respectively. After inserting a piece of new data (red), the jumped area may continuously skip over the original jump/cut-points. For example, the new jump from $p10$ skips over the old cut-point $p2^{\prime }$ and jump-point $p3^{\prime }$. Once the new chunking process finds a cut/jump-point in the original data ($p8^{\prime }$), the chunking process after the point will keep the same as the original chunking process.
