A polynomial time approximation scheme for embedding a directed hypergraph on a weighted ring

Jianping Li, Weidong Li, Lusheng Wang
2011 Journal of combinatorial optimization  
Given a directed hypergraph H = (V , E H ), we consider the problem of embedding all directed hyperedges on a weighted ring. The objective is to minimize the maximum congestion which is equal to the maximum product of the weight of a link and the number of times that the link is passed by the embedding. In this paper, we design a polynomial time approximation scheme for this problem. Keywords Directed hypergraph · Embedding · PTAS Introduction For a minimization problem and a polynomial
more » ... m A, if A can produce a feasible solution with objective value no more than α times the optimum solution value for any instances, then α is called performance guarantee or performance ratio of the algorithm A. A family of polynomial time approximation algorithms with performance guarantee 1 + for all fixed > 0 is called a polynomial time approximation scheme (PTAS). Due to the extensive applications in various areas, such as computer networks, multicast communication, parallel computation, electronic design automation, the
doi:10.1007/s10878-011-9387-1 fatcat:h6t6o7hgmfgfthmhaw4zd6euje