On-Line Competitive Coloring Algorithms


In the area of on-line algorithms the existence of competitive algorithms is one of the most frequently studied questions. However, competitive on-line graph coloring algorithms exist only for very restricted families of graphs. We introduce a new concept, called on-line competitive algorithms. Our main problem is whether on-line competitive coloring algorithms exist for all classes of graphs. This concept can be useful if somebody must design an on-line coloring algorithm and the input graph is only known to be in a specified class of graphs. In this case the designer want to get the best algorithm but this is usually hard. An on-line competitive algorithm offers less: it comes together with a function f such that for every graph in the class the number of colors it uses can be bounded by f(Ø (G)) where Ø (G) is the minimum number of colors can be achieved at all for that graph by any on-line algorithm (that algorithm may know the graph in advance). Of course, the smaller is f ..

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