Abstract
This paper proposes a method of estimating computational complexity of problem through analyzing its input condition for N-vehicle exploration problem. The N-vehicle problem is firstly formulated to determine the optimal replacement in the set of permutations of 1 to N. The complexity of the problem is factorial of N (input scale of problem). To balance accuracy and efficiency of general algorithms, this paper mentions a new systematic algorithm design and discusses correspondence between complexity of problem and its input condition, other than just putting forward a uniform approximation algorithm as usual. This is a new technique for analyzing computation of NP problems. The method of corresponding is then presented. We finally carry out a simulation to verify the advantages of the method: 1) to decrease computation in enumeration; 2) to efficiently obtain computational complexity for any N-vehicle case; 3) to guide an algorithm design for any N-vehicle case according to its complexity estimated by the method.
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Project supported by the State 973 Program (2006CB701306) and Key Laboratory of Management, Decision and Information Systems, CAS.
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Xia, X., Cui, Jc. A method of estimating computational complexity based on input conditions for N-vehicle problem. Acta Math. Appl. Sin. Engl. Ser. 26, 1–12 (2010). https://doi.org/10.1007/s10255-008-8811-5
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DOI: https://doi.org/10.1007/s10255-008-8811-5