A rectangular cartogram is a type of map where every region is a rectangle. The size of the rectangles is chosen such that their areas represent a geographic variable (e.g., population). Good rectangular cartograms are hard to generate: The area specifications for each rectangle may make it impossible to realize correct adjacencies between the regions and so hamper the intuitive understanding of the map.
We present the first algorithms for rectangular cartogram construction. Our algorithms depend on a precise formalization of region adjacencies and build upon existing VLSI layout algorithms. Furthermore, we characterize a non-trivial class of rectangular subdivisions for which exact cartograms can be computed efficiently. An implementation of our algorithms and various tests show that in practice, visually pleasing rectangular cartograms with small cartographic error can be generated effectively. 相似文献
This paper puts forward an integrated fuzzy simulation-fuzzy data envelopment analysis (FSFDEA) algorithm to cope with a special case of single-row facility layout problem (SRFLP). Discrete-event-simulation, a powerful tool for analyzing complex and stochastic systems, is employed for modeling different layout formations. Afterwards, a range-adjusted measure (RAM) is used as a data envelopment analysis (DEA) model for ranking the simulation results and finding the optimal layout design. Due to ambiguousness associated with the processing times, fuzzy sets theory is incorporated into the simulation model. Since the results of simulation are in the form of possibility distributions, the DEA model is treated on a fuzzy basis; therefore, a recent possibilistic programming approach is used to convert the fuzzy DEA model to an equivalent crisp one. The proposed FSFDEA algorithm is capable of modeling and optimizing small-sized SRFLP’s in stochastic, uncertain, and non-linear environments. The solution quality is inspected through a real case study in a refrigerator manufacturing company. 相似文献
A queue layout of a graph consists of a linear order of its vertices, and a partition of its edges into queues, such that no two edges in the same queue are nested. In this paper, we show that the n-dimensional hypercube Qn can be laid out using n−3 queues for n?8. Our result improves the previously known result for the case n?8. 相似文献
We consider the following problem: given a set of points in the plane, each with a weight, and capacities of the four quadrants, assign each point to one of the quadrants such that the total weight of points assigned to a quadrant does not exceed its capacity, and the total distance is minimized.
This problem is most important in placement of VLSI circuits and is likely to have other applications. It is NP-hard, but the fractional relaxation always has an optimal solution which is “almost” integral. Hence for large instances, it suffices to solve the fractional relaxation. The main result of this paper is a linear-time algorithm for this relaxation. It is based on a structure theorem describing optimal solutions by so-called “American maps” and makes sophisticated use of binary search techniques and weighted median computations.
This algorithm is a main subroutine of a VLSI placement tool that is used for the design of many of the most complex chips. 相似文献
This paper presents a mixed-integer programming formulation to find optimal solutions for the block layout problem with unequal departmental areas arranged in flexible bays. The nonlinear department area constraints are modeled in a continuous plane without using any surrogate constraints. The formulation is extensively tested on problems from the literature. 相似文献