On minimizing the maximum congestion for Weighted Hypergraph Embedding in a Cycle

SingLing Lee, Hann-Jang Ho
2003 Information Processing Letters  
The problem of Weighted Hypergraph Embedding in a Cycle (WHEC) is to embed the weighted hyperedges of a hypergraph as the paths in a cycle, such that the maximum congestion of any physical link in the cycle is minimized. A simpler version of this problem is the Weighted Graph Embedding in a Cycle (WGEC) that embeds the weighted edges of a normal graph as the paths in a cycle. The WHEC and WGEC problems have applications in design automation, parallel computing and computer communication. In
more » ... paper, we show that both WHEC and WGEC problems are NP-Complete. Also, we formulate WHEC problem as an integer linear programming (ILP). Therefore, the approximation solution can be obtained by using LP-relaxation and rounding heuristic. Our LP-approximation algorithm generates an embedding with congestion at most two times the optimal solution.
doi:10.1016/s0020-0190(03)00297-7 fatcat:f2jdxjoaszaqnlc3oxrd2n747e