Question

这是我之前提出的一些问题How to plan the most efficient route for patio lights和Christmas Light Route Efficiency (CS)的延续，关于我试图尽可能有效地覆盖带庭院灯的屏蔽结构。

以下是规则：

最小化光线重叠
每串灯都是234＆＃34;很长（这很重要，因为我不能开始新的灯光分支，除非它在另一个分支的末尾）。
将这些视为圣诞灯，你有男性和女性的一面：

start (male) end (female) =[}~~~o~~~o~~~o~~~o~~~o~~~o~~~o~~~{=] <- to outlet to other lights ->

因此，只要有一个女性供男性插入，多股可以菊花链，如下所示：
母插头必须通过公插头为下一缕灯供电，公插头不能给另一个插头供电。
以下是我的结构图：
Pink Circle =挂灯的地方（不，在10,11和12的交叉点没有悬挂灯的地方 - 这不是错误）。< / p>
＆＃34;开始＆＃34; =唯一可用的电源插座。
黄点=结构的一部分我想沿着灯运行。

根据我以前的问题，我开始研究＆＃34;路线效率问题＆＃34;算法。我使用这篇文章Solving Chinese Postman algorithm with eulerization开始，这引导我使用这段代码（感谢@DamianoFantini在我之前的帖子中帮助他正确设置图表）：

gg <- graph_from_edgelist(cbind(c(1:4, 6, 8, 10, 12, 14, 16:19, 1, 6, 8, 21, 12, 14, 5, 7, 9, 11, 13, 15), 
                                c(2:5, 7, 9, 11, 13, 15, 17:20, 6, 8, 10, 12, 14, 16, 7, 9, 11, 13, 15, 20)))
ll=matrix(
  c( 0,0,    75.25,0,    150.5,0,    225.8125,0,    302.8125,0, 
     0,-87,                                          302.8125,-87,
     0,-173.8125,                                    302.8125,-173.8125,
     0,-260.9375,                                    302.8125,-260.9375,
     16,-384.3125,                                   302.8125,-384.3125,
     16,-435.9575,                                   302.8125,-435.9375,
     16,-525.1875, 75.25,-525.1875, 150.5,-525.1875, 225.8125,-525.1875, 302.8175,-525.1875, 16, -260.9375),
  ncol=2,byrow=TRUE)

# SOURCE: https://stackoverflow.com/q/40576910/1152809
make.eulerian <- function(graph){
  # Carl Hierholzer (1873) had explained how eulirian cycles exist for graphs that are
  # 1) connected, and 2) contain only vertecies with even degrees. Based on this proof
  # the posibility of an eulerian cycle existing in a graph can be tested by testing
  # on these two conditions.
  #
  # This function assumes a connected graph.
  # It adds edges to a graph to ensure that all nodes eventuall has an even numbered. It
  # tries to maintain the structure of the graph by primarily adding duplicates of already
  # existing edges, but can also add "structurally new" edges if the structure of the
  # graph does not allow.

  # save output
  info <- c("broken" = FALSE, "Added" = 0, "Successfull" = TRUE)

  # Is a number even
  is.even <- function(x){ x %% 2 == 0 }

  # Graphs with an even number of verticies with uneven degree will more easily converge
  # as eulerian.
  # Should we even out the number of unevenly degreed verticies?
  search.for.even.neighbor <- !is.even(sum(!is.even(degree(graph))))

  # Loop to add edges but never to change nodes that have been set to have even degree
  for(i in V(graph)){
    set.j <- NULL

    #neighbors of i with uneven number of edges are good candidates for new edges
    uneven.neighbors <- !is.even(degree(graph, neighbors(graph,i)))

    if(!is.even(degree(graph,i))){
      # This node needs a new connection. That edge e(i,j) needs an appropriate j:

      if(sum(uneven.neighbors) == 0){
        # There is no neighbor of i that has uneven degree. We will
        # have to break the graph structure and connect nodes that
        # were not connected before:

        if(sum(!is.even(degree(graph))) > 0){
          # Only break the structure if it's absolutely nessecary
          # to force the graph into a structure where an euclidian
          # cycle exists:
          info["Broken"] <- TRUE

          # Find candidates for j amongst any unevenly degreed nodes
          uneven.candidates <- !is.even(degree(graph, V(graph)))

          # Sugest a new edge between i and any node with uneven degree
          if(sum(uneven.candidates) != 0){
            set.j <- V(graph)[uneven.candidates][[1]]
          }else{
            # No candidate with uneven degree exists!

            # If all edges except the last have even degrees, thith
            # function will fail to make the graph eulerian:
            info["Successfull"] <- FALSE
          }
        }

      }else{
        # A "structurally duplicated" edge may be formed between i one of
        # the nodes of uneven degree that is already connected to it.

        # Sugest a new edge between i and its first neighbor with uneven degree
        set.j <- neighbors(graph, i)[uneven.neighbors][[1]]
      }
    }else if(search.for.even.neighbor == TRUE & is.null(set.j)){
      # This only happens once (probably) in the beginning of the loop of
      # treating graphs that have an uneven number of verticies with uneven
      # degree. It creates a duplicate between a node and one of its evenly
      # degreed neighbors (if possible)
      info["Added"] <- info["Added"] + 1

      set.j <- neighbors(graph, i)[ !uneven.neighbors ][[1]]
      # Never do this again if a j is correctly set
      if(!is.null(set.j)){search.for.even.neighbor <- FALSE}
    }

    # Add that a new edge to alter degrees in the desired direction
    # OBS: as.numeric() since set.j might be NULL
    if(!is.null(set.j)){
      # i may not link to j
      if(i != set.j){
        graph <- add_edges(graph, edges=c(i, set.j))
        info["Added"] <- info["Added"] + 1
      }
    }
  }

  # return the graph
  (list("graph" = graph, "info" = info))
}

# Look at what we did
eulerian <- make.eulerian(gg)
g <- eulerian$graph

par(mfrow=c(1,2))
plot(gg)
plot(g)

这是代码的结果：

其中，我认为转换为此（但我是图形/算法菜鸟，如果我错了，请纠正我）：

显然，这里有一些问题：

我不知道每一缕灯的结束/开始应该在哪里（我认为算法也没有）
节点1独立供电。这在现实中是行不通的。所有权力必须来自＆＃34;开始＆＃34;位置。
似乎没有考虑到距离和结构。

有没有办法将这些约束添加到算法中？是否有其他算法可以使这更容易？

Answer 1

https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

您可以根据路径的不同度量使用不同的边缘数据来补充Dijkstra的算法，例如光重叠，或者例如每个边缘的灯光总照度。我想你可能需要在深角处有更高密度的光......

因此，目标可以是最低的光线区域，或障碍物的感知能见度，或者产生均匀环境光的路径。不管它是如何调整的，我相信Dijkstra的算法是一个非常标准的goto来找到这些东西。

更新：在创建最宽的覆盖区域的情况下，您需要生成树而不是最佳路径算法。这可能更多是您的想法：

https://en.wikipedia.org/wiki/Prim%27s_algorithm

如何规划露台灯最有效的路线第2部分

1 个答案: