超图嵌入图的最小拥挤问题展望

Prospectous for Embedding Hypergraph in a Cycle

We consider the problem of embedding hyperedges of a hypergraph as paths in a cycle such that the maximum congestion,the maximum number of paths that use any single edge in a cycle,is minimized. The Minimum Congestion Hypergraph Embedding in a Cycle problem is known to be NP-hard and its graph version,the Minimum Congestion Graph Embedding in a Cycle,is solvable in polynomial time. Furthermore,for the graph problem,a polynomial time approxima-tion scheme for the weighted version is known. For the hypergraphmodel, several approximation algorithms with a ratio of two have been previously published. A recent works on this problem reduced the approximation ratio to 1.5. We present a polynomial time approximation scheme in this paper,settling the debate regarding if the problem is polynomial time approximable