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匹配误差最小的两个图

[英]matching two graphs with the lowest error

原文 2017-10-20 12:37:54 8 2 algorithm/ optimization/ graph/ graph-algorithm

I have two graphs that I would like to match (I am not sure this is the world I'm looking for). 我有两个图表要匹配（我不确定这是我要寻找的世界）。

In my first graph nodes represents teams (node value represents the number of people in the team) and links represent how close teams are on a scale of 1 to 5. Two teams working a lot together will have a stronger link than two teams that work sometimes together. 在我的第一个图形中，节点表示团队（节点值表示团队中的人数），链接表示团队之间的亲密程度（从1到5）。两个在一起工作的团队比两个工作团队的联系更牢固有时在一起。

In my second graph nodes represent spaces (node value represents the available places in the space) and links represent how close the spaces are. 在我的第二张图中，节点表示空间（节点值表示空间中的可用位置），链接表示空间的接近程度。 If two spaces are on the same floor they will have a stronger link than two spaces that are not on the same floor. 如果两个空间位于同一层，则它们之间的联系将比两个不在同一层的空间更强。

I need to distribute the teams in the available spaces minimizing the distance between each linked team (two teams that have a strong link would be at the same floor for example). 我需要将团队分布在可用空间中，以最大程度地减少每个链接的团队之间的距离（例如，具有紧密链接的两个团队将位于同一楼层）。

My first question is : do you have a magic recipe that would solve this problem ? 我的第一个问题是：您有解决这个问题的灵丹妙药吗？ My second question : If not, do you know in what direction I need to check (algorithm that could be reworked, lectures, articles ...). 我的第二个问题：如果不是，您是否知道我需要检查的方向（可以重做的算法，讲座，文章...）。

Thank you very much. 非常感谢你。 Thoma 托马

2 个解决方案

To answer the question in part, apparently there is no known polynomial-time algorithm to solve the problem, as the problem includes the graph isomorphism problem as a subproblem. 要部分地回答该问题，显然没有已知的多项式时间算法可以解决该问题，因为该问题包括图形同构问题作为子问题。 This problem is neither known to be NP-complete nor has a polynomial algorithm been found. 既不知道这个问题是NP完全的，也没有找到多项式算法。

More precisely, suppose that the room graph is exactly the team graph, where edges are not weighted. 更准确地说，假设房间图恰好是团队图，其中边缘未加权。 As an optimal solution would match each team to the corresponding room, an algorithm for the problem in the question would be able to identify the input graphs to be isomorphic. 由于最佳解决方案将使每个团队与相应的会议室匹配，因此针对问题中的问题的算法将能够将输入图识别为同构。

After talking with some people, it seems that it might not be the best solution. 与某些人交谈之后，似乎这不是最佳解决方案。 I will look in the direction of solvers to be abble to have define constraints. 我将朝求解器的方向努力，使其具有定义的约束。

Thank you. 谢谢。