Abstract
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 c j times, each hyperedge h i has a profit p i 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 c j is k, we propose a \(\frac{3}{2}\)-approximation algorithm to handle the problem.
AMS Classifications: 90B10, 94C15.
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Li, J., Li, K., Law, K.C.K., Zhao, H. (2005). On Packing and Coloring Hyperedges in a Cycle. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_24
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DOI: https://doi.org/10.1007/11533719_24
Publisher Name: Springer, Berlin, Heidelberg
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