A 1.6 approximation algorithm for routing multiterminal nets
SIAM Journal on Computing
A bottom-up layout technique based on two-rectangle routing
Integration, the VLSI Journal
A linear time algorithm for optimal routing around a rectangle
Journal of the ACM (JACM)
Algorithms for routing around a rectangle
Discrete Applied Mathematics - Special issue: graphs in electrical engineering, discrete algorithms and complexity
Improved approximation algorithms for embedding hyperedges in a cycle
Information Processing Letters
A Simple Approximation Algorithm for Two Problems in Circuit Design
IEEE Transactions on Computers
Minimum-Congestion Hypergraph Embedding in a Cycle
IEEE Transactions on Computers
On minimizing the maximum congestion for Weighted Hypergraph Embedding in a Cycle
Information Processing Letters
A polynomial time algorithm for optimal routing around a rectangle
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
On packing and coloring hyperedges in a cycle
Discrete Applied Mathematics
A polynomial time approximation scheme for embedding hypergraph in a weighted cycle
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
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The Minimum Congestion Hypergraph Embedding in a Cycle (MCHEC) problem is to embed the hyperedges of a hypergraph as paths in a cycle with the same node set such that the maximum congestion (the maximum number of paths that use any single edge in the cycle) is minimized. The MCHEC problem has many applications, including optimizing communication congestions in computer networks and parallel computing. The problem is NP-hard. In this paper, we give a 1.8-approximation algorithm for the MCHEC problem. This improves the previous 2-approximation results. Our algorithm has the optimal time complexity O(mn) for a hypergraph with m hyperedges and n nodes. We also propose an algorithm which finds an embedding with the optimal congestion L^* for the MCHEC problem in O(n(nL^{*})^{L^{*}}) time. This improves the previous O((mn)^{L^{*}+1}) time algorithm.