For a set of n points in the plane, we consider the axis–aligned (p, k)-Box Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together contain at least n − k points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For ...

We present a notion of forcing that can be used, in conjunction with other results, to show that there is a Martin-Löf random set X such that X 6≥T ∅′ and X computes every K-trivial set.

Let V be a finite set of order v. A (v,k,A.) covering design of index A. and block size k is a collection of k-element subsets, called blocks, such that every 2-subset of V occurs in at least '}.. blocks. The covering problem is to determine the minimum number of blocks, a (v, k, A.), in a covering design. It is well known that a(v,k''}..)Lr~~=~'}..ll=(v,k,A.), where rxl is the smallest integer

We investigate the covering problem in RT spaces induced by the RosenbloomTsfasman metric, extending the classical covering problem in Hamming spaces. Some connections between coverings in RT spaces and coverings in Hamming spaces are derived. Several lower and upper bounds are established for the smallest cardinality of a covering code in an RT space, generalizing results by Carnielli, Chen an...

The Constructive Genetic Algorithm (CGA) was proposed by Lorena and Furtado [6], as an alternative to the traditional GAs approach. Particularly the CGA directly evaluates schemata, works with a dynamic population size, performs mutation in complete structures, and uses heuristics in schemata and/or structure representation. The schemata are evaluated and can be added to the population if they ...

This paper proposes a cluster partitioning technique to calculate improved upper bounds to the optimal solution of maximal covering location problems. Given a covering distance, a graph is built considering as vertices the potential facility locations, and with an edge connecting each pair of facilities that attend a same client. Coupling constraints, corresponding to some edges of this graph, ...

This article presents a column generation algorithm to calculate new improved lower bounds to the solution of maximal covering location problems formulated as a p-median problem. This reformulation leads to instances that are difficult for column generation methods. The traditional column generation method is compared with the new approach, where the reduced cost criterion used at the column se...

The distribution or delivery process is one factor that affect customer satisfaction as the goal of supply chain. In order for chain to be competitive in competition, time an important manage, so it could provide high service level value. One affects center location. A strategic location would facilitate and speed up process. This research discusses model determining made at right amount by ana...