Knapsack Problems for Wreath Products

In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under wreath product. As a consequence, we obtain the decidability of knapsack for free solvable groups. Finally, it is shown that for every non-trivial abelian group G, knapsack (as well as the related subset sum problem) for the wreath product G wr Z is NP-complete

An index for dynamic product promotion and the knapsack problem for perishable items

This paper introduces the knapsack problem for perishable items (KPPI), which concerns the optimal dynamic allocation of a limited promotion space to a collection of perishable items. Such a problem is motivated by applications in a variety of industries, where products have an associated lifetime after which they cannot be sold. The paper builds on recent developments on restless bandit indexation and gives an optimal marginal productivity index policy for the dynamic (single) product promotion problem with closed-form indices that yield estructural insights. The performance of the proposed policy for KPPI is investigated in a computational study.Dynamic promotion, Perishable items, Index policies, Knapsack problem, Festless bandits, Finite horizon, Marginal productivity index

Improvement of the ergonomical structure of Knapsack sprayer to propel cart sprayer (PCS)

A sprayer is a device used to spray a liquid projection mostly used in agriculture crop used to apply such as pesticides. The sprayer’s usage are based on the type of the background of the farmers scale in agriculture. Large scale of farmers will use the motorize sprayer that will help saving their time to pesticide a large are of corps [1]. Meanwhile, small scale of farmers will use a manual operated sprayer such as Knapsack Sprayer which it is a low cost, low maintenance and easy to use since it does not have engine when operated. Both type of the sprayer has its own advantages and disadvantages that will affect the user. Mainly the manual operated Knapsack Sprayer is a knapsack type, a burden that will make user carry the heavy load at their back while spraying pesticide. The weight of the mixture carried can be up to 17 kilograms depends on the density of the mixture whereas the safe weight lifting legalize by OSHA is 22.68 kilograms which the load almost near to its limit for average man and will affect the body locomotion and bones structure if carried in a long term period. Total sprayed area per full tank are 44.09 meters square [2]. The product that will be made are to counter this problem occur while using Knapsack Sprayer. This product using pushing force to spray the targeted area without having the user to carry a heavy burden while working

Knapsack problems in products of groups

The classic knapsack and related problems have natural generalizations to arbitrary (non-commutative) groups, collectively called knapsack-type problems in groups. We study the effect of free and direct products on their time complexity. We show that free products in certain sense preserve time complexity of knapsack-type problems, while direct products may amplify it. Our methods allow to obtain complexity results for rational subset membership problem in amalgamated free products over finite subgroups.Comment: 15 pages, 5 figures. Updated to include more general results, mostly in Section

Knapsack Problems in Groups

We generalize the classical knapsack and subset sum problems to arbitrary groups and study the computational complexity of these new problems. We show that these problems, as well as the bounded submonoid membership problem, are P-time decidable in hyperbolic groups and give various examples of finitely presented groups where the subset sum problem is NP-complete.Comment: 28 pages, 12 figure