Data structures and network algorithms
Data structures and network algorithms
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On the k-coloring of intervals
Discrete Applied Mathematics
Improved approximation algorithms for embedding hyperedges in a cycle
Information Processing Letters
A Simple Approximation Algorithm for Two Problems in Circuit Design
IEEE Transactions on Computers
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimum-Congestion Hypergraph Embedding in a Cycle
IEEE Transactions on Computers
On minimizing the maximum congestion for Weighted Hypergraph Embedding in a Cycle
Information Processing Letters
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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 ej 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 $\frac{3}{2}$-approximation algorithm to handle the problem. AMS Classifications: 90B10, 94C15.