A polynomial time approximation scheme for embedding a directed hypergraph on a ring
Information Processing Letters
A polynomial-time approximation scheme for embedding hypergraph in a cycle
ACM Transactions on Algorithms (TALG)
A polynomial time approximation scheme for embedding a directed hypergraph on a ring
Information Processing Letters
A polynomial time approximation scheme for embedding hypergraph in a weighted cycle
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
A polynomial time approximation scheme for embedding hypergraph in a weighted cycle
Theoretical Computer Science
An approximation algorithm for embedding a directed hypergraph on a ring
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
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The problem of Weighted Hypergraph Embedding in aCycle (WHEC) is to embed the weighted hyperedges of ahypergraph as the paths in a cycle, such that the maximumcongestion of any physical link in the cycle is minimized.A simpler version of this problem is the WeightedGraph Embedding in a Cycle (WGEC) that embeds theweighted edges of a normal graph as the paths in a cycle.The WHEC and WGEC problems have applicationsin design automation, parallel computing and computercommunication. In this paper, we first show that bothWHEC and WGEC problems are NP-Complete. Afterwardswe formulate the WHEC problem as an integer linearprogramming (ILP). Therefore, an approximation solutioncan be obtained by using LP-relaxation and roundingheuristic. Our LP-approximation algorithm generatesan embedding with congestion at most two times the optimalsolution. Finally, to guarantee the efficiency, wedevelop a linear-time approximation algorithm that alsoprovides a solution with the same worst case approximationbound as the LP-approximation.