title: Name of a variant of salesman problem.. I think
body: <p>I got faced with a problem that it seems for me is related to the salesman problem, but I cannot figure the correct way to solve it.</p>
  
  <p>I have N salesman and  M houses to visit (N is >= M ) each salesman departs from a different place, therefore have a different cost to reach each house. I have those distances.  </p>
  
  <p>How do I select the best set of salesmen to cover all the M houses?</p>
  
  <p>If I check all the possible permutations of salesmen in sets of M   in a cartesian product with all the houses it would work, but that  is absurdly  expensive to  any  large number of M or N</p>
  
  <p>Does anyone know if that problem has a specific name so I can search about it?</p>
  
  <p>Peter suggeseted the Hungarian algorithm  and while it does solve the problem, it seems the hungarian algorithm  solves a broader problem class. In the hungarian algorithm the costs are arbitrary and there is no constraints  or correlations between costs.</p>
  
  <p>On the problem I describe I can have salesman 1 ,2 and 3(S1,S2, and S3), assigned to  visit  houses 1 and 2 (h1 and H2).  Their positions might be S1 S2 h1 S3 h2 over a line for example. There is an implicit  correlation that between the costs because of how distances are laid on space. That would make indeed very important how the cost of the visit was measured (distance, that has those implicit correlations , or other  arbrtrary value).  </p>
  
  <p>I am still trying to discover if there is a name for this problem, that seems to be a sub class of the problem solved by the hungarian algorithm.</p>