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Unbounded knapsack3/22/2023 ![]() The result is tuple of bestValue, bestSize, bestItems, bestValues. GreedyKnapsackNd Non exact greedy N dimensional knapsack solver. HybridKnapsackNd NU algorithm called for worst exponential case of KB. It used in hybrid knapsack, and as greedy solver in knapsackNd. Gets size of knapsack, items, values, iterator counter array. ParetoKnapsack is implementation of KB-Nemhauser-Ullman algorithm. It is used in partitionN method in the strict group size case. KnapsackNd, expects the single tuple as size constrains of knapsack, items as tuples of dimensions, values, iterator counter array. ![]() Which used in greedy solver in knapsackNd. Knapsack, gets size of knapsack, items, values, iterator counter array. The result is tuple of bestValue, bestItems. It requires the following parameters: size of knapsack, items, iterator counter array. SubsKnapsack, which used in partitionN as set grouping operator. ![]() Hybrid partition uses KB-NU algorithm as grouping operator. The result is tuple of quotients, reminder, optimizationCount. HybridPartitionN, which gets number set to partition, partitions number or list of particular sizes of each partition, strict partition group size. PartitionN, which gets number set to partition, partitions number or list of particular sizes of each partition, strict partition group size. The Out folder is considered as output for tests and reports if flags/flags.py printToFile set to true. The tests directory has tests, and performance report generators. The API/main.py file has API for described algorithms. That algorithm runtime is M times slower than the subset sum problem. The run time complexity is exponential in number of partition. The algorithms for multiple knapsack that is exponential in numbers of knapsacks. The M equal-subset-sum of N integer number set that is exponential in M only. The greedy M independent dimension knapsack algorithm that exponential in reduced N that depends on given constraint. A non exact greedy algorithm was introduced for general case. The counting and non increasing order cases were solved in polynomial time. The exponential algorithm for T independent dimensions unbounded 1-0 knapsack problem. The polynomial hybrid KB-NU algorithm for unbounded 1-0 knapsack problem for positive integer and rational weights and profits. The exponential KB algorithm for unbounded 1-0 knapsack problem for positive integer and rational weights and profits. The enhanced exponential implementation of Nemhauser-Ullmann NU algorithm. The polynomial time and space algorithm for unbounded subset sum knapsack problem for positive integer and rational numbers. This research includes the implementation of the algorithms in both python and cpp, as well as performance analysis and reports. The restriction on integer input types was also removed. Special cases were solved using polynomial time and integrated into a new partition algorithm.Īdditionally, the algorithm for the equal subset problem was optimized to exhibit exponential complexity only in terms of the number of partitions. ![]() The 1-0 unbounded knapsack problem, a classic problem in dynamic programming, was extended to incorporate rational numbers and multiple dimensions. Rethinking the knapsack and set partitions.
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