|Author||Delbot, Franois ♦ Laforest, Christian|
|Source||ACM Digital Library|
|Publisher||Association for Computing Machinery (ACM)|
|Subject Domain (in DDC)||Computer science, information & general works ♦ Computer programming, programs & data|
|Subject Keyword||Differential approximation ♦ Mean analysis ♦ Vertex cover ♦ Worst case approximation|
|Abstract||The vertex cover is a well-known NP-complete minimization problem in graphs that has received a lot of attention these last decades. Many algorithms have been proposed to construct vertex cover in different contexts (offline, online, list algorithms, etc.) leading to solutions of different level of quality. This quality is traditionally measured in terms of approximation ratio, that is, the worst possible ratio between the quality of the solution constructed and the optimal one. For the vertex cover problem the range of such known ratios are between 2 (conjectured as being the smallest constant ratio) and Δ, the maximum degree of the graph. Based on this measure of quality, the hierarchy is almost clear (the smaller the ratio is, the better the algorithm is). In this article, we show that this measure, although of great importance, is too macroscopic and does not reflect the practical behavior of the methods. We prove this by analyzing (known and recent) algorithms running on a particular class of graphs: the paths. We obtain closed and exact formulas for the mean of the sizes of vertex cover constructed by these different algorithms. Then, we assess their quality experimentally in several well-chosen class of graphs (random, regular, trees, BHOSLIB benchmarks, trap graphs, etc.). The synthesis of all these results lead us to formulate a “practical hierarchy” of the algorithms. We remark that it is, more or less, the opposite to the one only based on approximation ratios, showing that worst-case analysis only gives partial information on the quality of an algorithm.|
|Age Range||18 to 22 years ♦ above 22 year|
|Education Level||UG and PG|
|Learning Resource Type||Article|
|Publisher Place||New York|
|Journal||Journal of Experimental Algorithmics (JEA)|
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