An average running time analysis of a backtracking algorithm to calculate the measure of the union of hyperrectangles in $d$ dimensions
نویسندگان
چکیده
[2] are known. In this paper, we propose a backtracking algorithm to solve MEASURE, analyze its average running time ((4) to (7) in Section 5), and show that the backtracking algorithm is more efficient than the former algorithms[1, 2] when P Q and there are many large hy-perrectangles ((8) and (9) in Section 6). By the way, MEASURE can be considered a generalization of the problem to count the number of unsatisfy-ing assignments of the satisfiability problem SAT, which is denoted by COUNT-SAT in this paper. For example, the COUNT-SAT problem to count the number (denoted by m
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