论文信息 - Covering edges by cliques with regard to keyword conflicts and intersection graphs

Covering edges by cliques with regard to keyword conflicts and intersection graphs

Kellerman has presented a method for determining keyword conflicts and described a heuristic algorithm which solves a certain combinatorial optimization problem in connection with this method. This optimization problem is here shown to be equivalent to the problem of covering the edges of a graph by complete subgraphs with the objective of minimizing the number of complete subgraphs. A relationship between this edge-clique-cover problem and the graph coloring problem is established which allows algorithms for either one of these problems to be constructed from algorithms for the other. As consequences of this relationship, the keyword conflict problem and the edge-clique-cover problem are shown to be NP-complete, and if P ≠ NP then they do not admit polynomial-time approximation algorithms which always produce solutions within a factor less than 2 from the optimum.

[1] David C. Wood,et al. A technique for colouring a graph applicable to large scale timetabling problems , 1969, Computer/law journal.

[2] David S. Johnson,et al. Approximation algorithms for combinatorial problems , 1973, STOC.

[3] Frank Harary,et al. Graph Theory , 2016 .

[4] Richard M. Karp,et al. On the Computational Complexity of Combinatorial Problems , 1975, Networks.

[5] D. J. A. Welsh,et al. An upper bound for the chromatic number of a graph and its application to timetabling problems , 1967, Comput. J..

[6] Alfred V. Aho,et al. The Design and Analysis of Computer Algorithms , 1974 .

[7] David S. Johnson,et al. The Complexity of Near-Optimal Graph Coloring , 1976, J. ACM.