A polynomial time approximation scheme for embedding hypergraph in a weighted cycle
Theoretical Computer Science
A polynomial time approximation scheme for embedding a directed hypergraph on a weighted ring
Journal of Combinatorial Optimization
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We consider the problem of embedding weighted hyperedges of a hypergraph as paths in a cycle on the same number of vertices, such that the maximum congestion of any physical link of the cycle is minimized. The problem, called weighted hypergraph embedding in a cycle (WHEC), is known to be NP-complete even when each hyperedge is unweighted or each weighted hyperedge contains exactly two vertices. In this paper, we propose an improved rounding algorithm for the WHEC problem to provide a solution with an approximation bound of $1.5(opt+w_{max})$, where $opt$ represents the optimal value of the problem and $w_{max}$ denotes the largest weight of hyperedges. For any fixed $\varepsilon 0$, we also present a polynomial time algorithm to provide an embedding whose congestion is at most $(1.5+\varepsilon)$ times the optimum. This improves previous results for the general WHEC problem.