In this paper we suggest a new efficient technique for solving integer knapsack problems. Our algorithms can be seen as application of Fast Fourier Transform to generating functions of integer polytopes. Using this approach, it is possible to count the number of boolean solutions of a single n-dimensional Diophantine equation 〈a, x〉 = b in O(‖a‖1 ln ‖a1‖ ln n) operations. Another application ex...

We study the problem of predicting a set or list of options under knapsack constraint. The quality of such lists are evaluated by a submodular reward function that measures both quality and diversity. Similar to DAgger (Ross et al., 2010), by a reduction to online learning, we show how to adapt two sequence prediction models to imitate greedy maximization under knapsack constraint problems: CON...

The knapsack problems are a classic NP-hard problem in the combinational optimization. Inspired by the conclusion of the cognitive psychology about the human memory system, a Tabu Search method based on Double Tabu-List (DTL-TS) has been proposed to solve it. With the addition of the search strategy of intensification and diversification, the excellent experiment results have been gotten. Compa...

This paper presents a heuristic to solve the Multidimensional Multiple-choice Knapsack Problem (MMKP), a variant of the classical 0–1 Knapsack Problem. We apply a transformation technique to map the multidimensional resource consumption to single dimension. Convex hulls are constructed to reduce the search space to find the near-optimal solution of the MMKP. We present the computational complex...

This paper introduces a knapsack cryptosystem based on the problem of discrete logarithm. The proposed algorithm obtains the public knapsack values by finding the discrete logarithms of the secret knapsack ones. Also, it encrypts the message block by obtaining its binary bits and then computing the modular multiplication of the public knapsack values corresponding to the 1-bits of the binary fo...

We introduce methods to count and enumerate all maximal independent, all maximum independent sets, and all independent sets in threshold graphs and k-threshold graphs. Within threshold graphs and k-threshold graphs independent sets correspond to feasible solutions in related knapsack instances. We give several characterizations for knapsack instances and multidimensional knapsack instances whic...

The definitions of optimal preventive and corrective maintenance of electric power distribution networks can be seen as a special case of a knapsack problem. This paper proposes a dynamic programming approach to deal with this problem. The approach is developed for one or more years of planning horizon. Case studies compare the optimal dynamic programming approach with an heuristic method.

the facet of knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. strong covers for facets of knapsack ploytope has been developed in the first pa...

In the incremental knapsack problem (IK), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of T periods and the capacity of the knapsack is Bt in period t for t = 1, . . . , T . We are also given a set S of N items to be placed in the knapsack. Item i has a value of vi and a weight of wi that is independent of the time period. At any time period...