In this paper, we consider a multi-hop sensor network, where the network topology is a tree, TDMA (time division multiple access) is employed as medium access control, and all data generated at sensor nodes are delivered to a sink node (the base station) located on the root of the tree through the network. It is reported that if a transmission schedule that avoids interference between sensor nodes completely can be computed, TDMA is preferable to CSMA/CA (carrier sense multiple access with collision avoidance) in performance. In general, the TDMA scheduling problem to find the shortest schedule is formulated as a combinatorial optimization problem, where each combination corresponds to a schedule. However, solving such a combinatorial optimization problem is difficult, especially for large-scale multi-hop sensor networks. The reason of the difficulty is that the number of the combinations increases exponentially with the increase of the number of nodes. In this paper, to formulate the TDMA scheduling problem, we propose a min-max model and a min-sum model. The min-max model yields the shortest schedule, but it is difficult to solve large-scale problems. The min-sum model does not guarantee providing the shortest schedule; however, it may give us good schedules over a short amount of computation time, compared to the min-max model. Numerical examples show that the min-sum model can provide good schedules in a reasonable CPU time, even when the min-max model fails to compute the shortest schedule in a reasonable CPU time.
In this paper, we consider a multi-hop sensor network, where the network topology is a tree, TDMA is employed as medium access control, and all data generated at sensor nodes are delivered to a sink node located on the root of the tree through the network. It is reported that if a transmission schedule that avoids interference between sensor nodes completely can be computed, TDMA is preferable to CSMA/CA in performance. However, solving the scheduling problem for TDMA is dicult, especially, in large-scale multi-hop sensor networks. In this paper, to formulate the scheduling problem for TDMA, we propose min-max model and min-sum model. While the min-max model yields the shortest schedule under the constraints, the min-sum model does not guarantee providing the shortest schedule. Numerical examples show that the min-sum model can provide good schedules in a reasonable CPU time, even when the min-max model fails to compute the shortest schedule in a reasonable CPU time.
Data visualization is highly needed in urban and regional planning. One popular option for describing data is through radar charts, as they make comparisons much easier to do. On the other hand, radar charts can also be misleading as the larger the area graph is, the better it is valued. However, that is incorrect since the area graph can easily be changed if the order of the axes changes or if there is a correlation between the neighboring axes. In this paper, we will reveal how the area graphs change, focusing on the correlation of spatial data.
We can use many kinds of metrics when we use Voronoi diagrams for analyzing in urban and regional models. As well known, the circular-radial metric is suitable to formulate several analytical models for many large scale urban fields. However, there exist few previous studies to construct the Voronoi diagram for circular-radial metric. In this paper, the algorithm of drawing the Voronoi diagram for circular-radial metric is concerned. For the first, we introduce analytical derivation of Voronoi borders, which is cumbersome procedure. In the next, we suggest the incremental method for drawing the Voronoi diagram based on the Voronoi borders result.
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