Optimizing some constructions with bars: new geometric knapsack problems
نویسندگان
چکیده
منابع مشابه
Optimizing some constructions with bars: new geometric knapsack problems
A set of vertical bars planted on given points of a horizontal line defines a fence composed of the quadrilaterals bounded by successive bars. A set of bars in the plane, each having one endpoint at the origin, defines an umbrella composed of the triangles bounded by successive bars. Given a collection of bars, we study how to use them to build the fence or the umbrella of maximum total area. W...
متن کاملSome Very Easy Knapsack / Partition Problems
Consider the problem of partitioning a group of b indistinguishable objects into subgroups, each of size at leastl and at most u. The objective is to minimize the additive separable cost of the partition, where the cost associated with a subgroup of size j is c(j). In the case that c(.) is convex, we show how to solve the problem in O(log u-/ + 1) steps. In the case that c(.) is concave, we sol...
متن کاملSome Geometric Clustering Problems
This paper investigates the computational complexity of several clustering problems with special objective functions for point sets in the Euclidean plane. Our strongest negative result is that clustering a set of 3k points in the plane into k triangles with minimum total circumference is NP-hard. On the other hand, we identify several special cases that are solvable in polynomial time due to t...
متن کاملKnapsack problems with setups
RÉSUMÉ : We consider two variants of knapsack problems with setups arising as subproblems in a DantzigWolfe decomposition approach to more complex combinatorial optimization problems. In the multiple-class binary knapsack problem with setups, items are partitioned into classes whose use implies a setup cost and associated capacity consumption. Item weights are assumed to be a multiple of their ...
متن کاملCombining Arithmetic and Geometric Rounding Techniques for Knapsack Problems
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding. As an application of these techniques, we present a faster polynomial time approximation scheme requiring only linear storage, that computes an approximate s...
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: Journal of Combinatorial Optimization
سال: 2014
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-014-9816-z