CSCE686 Homework HW4


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CSCE686 Homework
a) (40pts) Design & Improve the AFIT graphprogram for the MIS algorithm.
“Educational Objective: develop an understanding and ability to use the
mapping PD (MIS) into AD (gs-dfs/bt) via our top-down design process
using Christofides’ MIS algorithm design and implementation from our
gs-dfs/bt algorithm specification.” “A software engineer in a closet
should now understand the total development from PD/AD integration
to pseudo code to code step by step with additional heuristics.”
a.1 (30 points) Incorporate at least the ordering heuristic and the
pivoting heuristic** {Andrade, Christofides Bron Kerbisch), Pelillo, …}
into the graphprogram MIS by explicitly following our top down PD/AD
search element design approach. Show this PD/AD design explicitly
integrating step-by-step these creative new heuristics top-down into
functional pseudo code. Extend the use of the standard search elements
into the given graphprogram code as well as the step notation from the
new pseudo code to C++ code with your new heuristics.
Develop the PD/AD design using the ordering and pivoting heuristics
for a MIS/Clique algorithm implemented in a different programming
language. Of course, include standard search elements throughout the
new heuristic design development as appropriate (including
a.2 (10 points) Test and compare MIS results with/without Heuristics
over some relatively small, medium and large PD graphs (From
Problem 3 and/or DIMACS,BHOSLIB, …). Consider planer, nonplaner, perfect, circle, bipartite, permutation, and chordal graphs? For
medium PD graph size, generate search graph.
Report: Discuss the above top-down design, implementation, and
testing efforts concisely! (for testing follow Barr,Talbi1.7)

*consider an ordering of the nodes for selection based upon
number of connections (max, min) in an attempt to find the maximum
independent set. “Heuristic impact?” [complexity?]
** Add an algorithm to implement Christofides Equation 3.9, page 34.
This is defined as “pivoting” in some descriptions of the BK algorithm
(see Wikipedia and other references). This additional heuristic as stated
by Christofides can force the backtracking set earlier. “Heuristic
impact?” [complexity?]

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