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Recently, a simple yet powerful branch-and-bound method called Efficient Subwindow Search (ESS) was developed to speed up sliding window search in object detection. A major drawback of ESS is that its computational complexity varies widely from O(n2) to O(n4) for n × n matrices. Our experimental experience shows that the ESS's performance is highly related to the optimal confidence levels which indicate the probability of the object's presence. In particular, when the object is not in the image, the optimal subwindow scores low and ESS may take a large amount of iterations to converge to the optimal solution and so perform very slow. Addressing this problem, we present two significantly faster methods based on the linear-time Kadane's Algorithm for 1D maximum subarray search. The first algorithm is a novel, computationally superior branch-and-bound method where the worst case complexity is reduced to O(n3). Experiments on the PASCAL VOC 2006 data set demonstrate that this method is significantly and consistently faster (approximately 30 times faster on average) than the original ESS. Our second algorithm is an approximate algorithm based on alternating search, whose computational complexity is typically O(n2). Experiments shows that (on average) it is 30 times faster again than our first algorithm, or 900 times faster than ESS. It is thus well-suited for real time object detection.