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POAlgorithm for Least Edge Intersections
 

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    <p>(Before anyone asks, it's not homework.)</p> <p>Say you have 2 Arrays <code>y0</code> and <code>y1</code> where</p> <p><code>y0 = [1,2,3,4,5,6]</code> and <code>y1 = [2,1,6,3,4,5]</code></p> <p>Notice <code>y0[0] = y1[1] = 1</code>, it essentially means <code>y0[0]</code> is connected to <code>y1[1]</code>. Similarly, <code>y0[2] = y1[3] = 3</code> so they are "connected" as well. </p> <p><img src="https://i.stack.imgur.com/wYkkr.png" alt="alt text"><em>(Image courtesy : belisarius)</em></p> <p>Each element in one array has a corresponding entry in the second array. <em>Imagine each element in the array as a <strong>vertex</strong>, and these connections as <strong>Edges</strong> being drawn from one array to the other.</em></p> <p>I need to find a set of <strong>edges</strong> (of maximum size) such that none of the "edges" (or lines) will intersect.</p> <p>In the above example, notice,</p> <ol> <li><code>Edge 1</code> and <code>Edge 2</code> will intersect. </li> <li><code>Edge 6</code> will intersect with <code>Edge 3, Edge 4, Edge 5</code>.</li> </ol> <p>Therefore, the solution can be be <code>1,3,4,5</code> or <code>2,3,4,5</code> (size = 4) since none of those lines will intersect each other. There can be multiple solutions, but I need just one.</p> <p>My Question, Is there any known CS Problem that resembles this? What algorithm should i be using?</p> <p>I've tried to explain my problem with an example, however, incase it's still not clear i'll clarify any queries. Thanks in advance.</p>
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    1. COThis seems connected to the question of whether a graph is planar and, if not, what its largest planar subgraph is. I don't know of any algorithms for it, though.
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    2. COThis is a direct graph. Do you mean y0[0] is connected to y1[0]? Because if y0[0] = y1[1] = 1 that's a point so you can't form an edge from a vertex to itself. When you say intersect do you mean a path that creates a cycle? For example, if you walked from a vertex along the connected edges you could come back your starting vertex? And this problem is finding all cycles regardless if they are connected to each other?
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    3. CO@chubbard, no, by intersection, i was implying a geometric line intersection.And no, `y0[0]` is not connected to `y1[0]`...
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