title: Updating Shortest path distances matrix if one edge weight is decreased
body: <p>We are given a weighed graph G and its Shortest path distance's matrix delta. So that delta(i,j) denotes the weight of shortest path from i to j (i and j are two vertexes of the graph).
  delta is initially given containing the value of the shortest paths. Suddenly weight of edge E is decreased from W to W'. How to update delta(i,j) in O(n^2)? (n=number of vertexes of graph)
  The problem is NOT computing all-pair shortest paths again which has the best O(n^3) complexity. the problem is UPDATING delta, so that we won't need to re-compute all-pair shortest paths.</p>
  
  <p>More clarified : All we have is a graph and its delta matrix. delta matrix contains just value of the shortest path. now we want to update delta matrix according to a change in graph: decreased edge weight. how to update it in O(n^2)?</p>