Shift-and-Merge Technique for the DP Solution of the Backpacker Problem
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چکیده
We formulate the ‘backpacker problem’ as an extension of the binary knapsack problem, and present two dynamic programming (DP) algorithms to solve this problem to optimality. Firstly, we propose a DP algorithm that solves the problem in pseudo polynomial time. Based on the observation that the optimal objective function is a step function of the knapsack capacity, we present an improved, ‘shift-and-merge’ DP algorithm. Although this technique does not change the worst case complexity, in practical computation the computing time is significantly reduced. We implement the DP and shift-and-merge DP algorithms in ANSI-C language, and evaluate the performance of these algorithms for various type and size of instances, including comparison against MIP solvers.
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تاریخ انتشار 2010