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CSC 373            Homework Exercise 5 -- Marking Scheme          Fall 2008
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NOTE TO STUDENTS:

You will find below the marking scheme used for your homework, including
the meaning of marking codes and number of marks associated with each one.
This file also contains my instructions to the marker (so you can get an
idea of how the homework was marked) and the marker's comments about each
question.

Please take the time to read this carefully before you ask questions about
the grading of your homework.


NOTE TO MARKER:

Be picky!  On any homework, it is the responsibility of students to show
that they understand how to solve each problem and to write up their
answers carefully.  At the same time, keep in mind that exercises are worth
only 1.5% of the final grade, so your marking should be somewhat coarse.
And remember that marking is not just about evaluating the students's
performances, but also about giving them feedback so that they can learn
from their mistakes.  This is especially important for students who made
numerous or more serious mistakes, as they are likely to need more feedback
in order to understand why their answers were incorrect.

For each question, I list solution elements with an associated code for
writing on student papers (the letter(s) between underscores _) and a
number of marks.  There are also general errors (with associated codes)
given below, with a maximum number of marks to take off for each type of
general error (as a percentage of the value of the question).  You will
likely encounter other common errors, or maybe decide to break down the
marking scheme further.  Simply make note of these changes/additions to
the marking scheme, and introduce new code letters (or short words) to
allow you to quickly give accurate feedback to the students (both in terms
of what they did wrong and how many marks it cost them).


GENERAL ERRORS (marked negatively, in addition to any other errors):

    _N_otation [up to 20%]:  incorrect/ambiguous notation

    _V_agueness [up to 20%]:  incorrect/unjustified/vague claim


1.  [6 marks]

    _S_tructure [1 mark]:  clear attempt to find a maximum flow and
        construct a minimum cut based on that flow, following the
        techniques given in class and showing the computation

    _F_low [2 mark]:  correct maximum flow constructed

    _C_ut [2 marks]:  correct minimum cut found

    _J_ustification [1 mark]:  good justification of correctness

    Marker's Comments:  Most common error: not showing augmenting paths.


2.  [9 marks]

    _S_tructure [2 marks]:  clear attempt to give an explicit algorithm to
        compute a maximum flow in a network with vertex capacities, and to
        argue that the algorithm is correct and runs in polytime

    _A_lgorithm [3 marks]:  correct (and complete) polytime algorithm

    _C_orrectness [3 marks]:  good explanation of the algorithm's
        correctness

    _R_untime [1 mark]:  good analysis of the algorithm's runtime

    Marker's Comments:  Biggest problem: not giving runtime analysis (only
        one person analyzed the runtime), and showing equivalence (often,
        people didn't argue correctness or did so in only one direction).