منابع مشابه
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.
متن کاملKnapsack problems in products of groups
The classic knapsack and related problems have natural generalizations to arbitrary (non-commutative) groups, collectively called knapsacktype 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 obtai...
متن کاملMulti-dimensional Knapsack Problems
This chapter reviews our recent work on applying hybrid collaborative techniques that integrate Branch and Bound (B&B) and Memetic Algorithms (MAs) in order design effective heuristics for the Multidimensional Knapsack Problem (MKP). To this end, let us recall that Branch and Bound (B&B) [1] is an exact algorithm for finding optimal solutions to combinatorial problems, that, basically works by ...
متن کاملYet harder knapsack problems
Already 30 years ago, Chvátal has shown that some instances of the zero-one knapsack problem cannot be solved in polynomial time using a particular type of branch-and-bound algorithms based on relaxations of linear programs together with some rudimentary cutting-plane arguments as bounding rules. We extend this result by proving an exponential lower bound in a more general class of branch-and-b...
متن کاملOnline Knapsack Problems
Since no competitive online algorithms exist for general knapsack problems, we consider online variants of knapsack problems with two assumptions: (i) the weight of each item is very small compared to the knapsack capacity; (ii) the value-to-weight ratio of each item is lower and upper bounded by two positive constants L and U . We design a deterministic threshold-based algorithm for the online...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2014
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2014-02880-9