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Recently, images on the Web and personal computers are prevalent around the humanpsilas life. To retrieve effectively those images, there are many AIA (Automatic Image Annotation) algorithms. However, it still suffers from low-level accuracy since it couldnpsilat overcome the semantic-gap be tween low-level features (dasiacolorpsila,dasiatexturepsila and dasiashapepsila) and high-level semantic meanings (e.g., dasiaskypsila,dasiabeachpsila). Namely, AIA techniques annotates images with many noisy key words. Refinement process has been appeared in these days and it tries to remove noisy keywords by using Knowledge-base and boosting candidate keywords. Because of limitless of candidate keywords and the incorrectness of web-image textual descriptions, this is the time we need to have deterministic polynomial time algorithm. We show that finding optimal solution for removing noisy keywords in the graph is NP-Complete problem and propose new methodology for KBIAR (Knowledge Based Image Annotation Refinement) using the randomized approximation graph algorithm as the general deterministic polynomial time algorithm.