algorithm - "Assignment Problem" solution question -

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i reading through solution assignment problem here: http://www.topcoder.com/tc?module=static&d1=tutorials&d2=hungarianalgorithm

i understand o(n3) solution), had question easier o(n4) solution.

perhaps misunderstood notation, when goes modify weights in step 2 -- why doesn't weight w1->j2 increase same way w2->j1 increases.

can better explain notation in rule defined in

enter image description here

it looks 2 logical symbols supposed "and" , "xor" respectively. xor symbol chosen looks more inclusive or, typo. see http://en.wikipedia.org/wiki/exclusive_or of less confusing alternatives.

with interpretation, have following possibilities:

  1. neither i nor j in v. first case.
  2. i in v, j not. second case.
  3. i not in v, j is. second case.
  4. both i , j in v. third case.

as see, cases covered, , there no ambiguity.


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