title: Minimize maximum manhattan distance of a point to a set of points
body: <p>For 3 points in 2D : </p>
  
  <pre><code>P1(x1,y1), 
  P2(x2,y2), 
  P3(x3,y3) 
  </code></pre>
  
  <p>I need to find a point <code>P(x,y)</code>, such that the maximum of the manhattan distances </p>
  
  <pre><code>max(dist(P,P1), 
      dist(P,P2), 
      dist(P,P3))
  </code></pre>
  
  <p>will be minimal.</p>
  
  <p>Any ideas about the algorithm?</p>
  
  <p>I would really prefer an exact algorithm.</p>