2 - A Plan of Attack
Published online by Cambridge University Press: 05 February 2012
Summary
Strategy without tactics is the slowest route to victory. Tactics without strategy is the noise before defeat.
Sun Tzu, The Art of WarW. I. B. Beveridge, in his classic guidebook for young scientists [7], likens scientific research “to warfare against the unknown”:
The procedure most likely to lead to an advance is to concentrate one's forces on a very restricted sector chosen because the enemy is believed to be weakest there.Weak spots in the defence may be found by preliminary scouting or by tentative attacks.
This chapter is about developing small- and large-scale plans of attack in algorithmic experiments.
To make the discussion concrete, we consider algorithms for the graph coloring (GC) problem. The input is a graph G containing n vertices and m edges. A coloring of G is an assignment of colors to vertices such that no two adjacent vertices have the same color. Figure 2.1 shows an example graph with eight vertices and 10 edges, colored with four colors. The problem is to find a coloring that uses a minimum number of colors – is 4 the minimum in this case?
When restricted to planar graphs, this is the famous map coloring problem, which is to color the regions of a map so that adjacent regions have different colors. Only four colors are needed for any map, but in the general graph problem, as many as n colors may be required.
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- A Guide to Experimental Algorithmics , pp. 17 - 49Publisher: Cambridge University PressPrint publication year: 2012