For a hypergraph and k different colors, we study the problem of packing and coloring some hyperedges of the hypergraph as paths in a cycle such that the total profit of the chosen hyperedges are maximized, here each link e j on the cycle is used at most cj times, each hyperedge hi has a profit pi and any two paths, each spanning all vertices of its corresponding hyperedge, must receive different colors if they share a link. This new problem arises in optical communication networks and it is called the Maximum Profits of Packing and Coloring Hyperedges in a Cycle problem (MPPCHC). In this paper, we prove that the MPPCHC problem is NP-hard and present a 2-approximation algorithm. For the special case, where each hyperedge has the same profit and each capacity Cj is k, we propose a 3/2-approximation algorithm to handle the problem. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Li, J., Li, K., Law, K. C. K., & Zhao, H. (2005). On packing and coloring hyperedges in a cycle. In Lecture Notes in Computer Science (Vol. 3595, pp. 220–229). Springer Verlag. https://doi.org/10.1007/11533719_24
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