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update README.md
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kittobi1992 committed Jul 24, 2023
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Expand Up @@ -60,7 +60,7 @@ The sum-of-external-degree metric is similar to the connectivity metric, but doe
![steiner_tree](https://github.com/kahypar/mt-kahypar/assets/9654047/926ef7d7-bb6b-4959-af0c-75ebd6f6299f)

The Steiner tree metric is the most versatile metric that we provide at the moment. A Steiner tree is a tree with minimal weight that spans a subset of the nodes on a graph. When optimizing the Steiner tree metric, we map the node set of a hypergraph H onto the nodes of a target graph G. The objective is to minimize the total weight of all Steiner trees induced by the nets of H on G.
For a net e, dist(Λ(e)) is the weight of the minimal Steiner tree connecting the blocks Λ(e) of net e on G. The Steiner tree metric can be used to accurately model wire-lengths in VLSI design or communication costs in distributed systems when some processors do not communicate with each other directly or with different speeds.
For a net e, dist(Λ(e)) is the weight of the minimal Steiner tree connecting the blocks Λ(e) spanned by net e on G. The Steiner tree metric can be used to accurately model wire-lengths in VLSI design or communication costs in distributed systems when some processors do not communicate with each other directly or with different speeds.

Note that finding a Steiner tree is an NP-hard problem. We therefore enforce a strict upper bound on the number of nodes of the target graph G which are 64 nodes at the moment. If you want to map a hypergraph onto larger targer graphs, you can use recursive multisectioning. For example, if you want to map a hypergraph onto a graph with 4096 nodes, you can first partition the hypergraph into 64 blocks, and then map each block of the partition onto a subgraph of target graph with 64 nodes. We plan to integrate this technique into Mt-KaHyPar in the future.

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