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In this paper, we consider the k-correlation clustering problem on uniform hypergraphs. Given an edge-weighted r-uniform hypergraph H(V, E) where the edges are labeled either positive or negative with non-negative weights, we want to partition the nodes into at most k-clusters to maximize agreements: the total weights of positive edges within clusters and negative edges between clusters. This problem is NP-Hard. We design an approximation algorithm with the approximation ratio \(\frac{A_{k}^{r}}{k^{r}-k+A_{k}^{r}}\) , here \(A_{k}^{r}=k(k-1)(k-2)\cdots (k-r+1)\) is the number of r permutations from k elements.

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Approximation Algorithms on k-Correlation Clustering of Uniform Hypergraphs

  • 会议论文

  • 发表日期：

    2025年

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  • Zhongzheng Tang,
  • Yaxuan Li,
  • Zhuo Diao

摘要

In this paper, we consider the k-correlation clustering problem on uniform hypergraphs. Given an edge-weighted r-uniform hypergraph H(V, E) where the edges are labeled either positive or negative with non-negative weights, we want to partition the nodes into at most k-clusters to maximize agreements: the total weights of positive edges within clusters and negative edges between clusters. This problem is NP-Hard. We design an approximation algorithm with the approximation ratio \(\frac{A_{k}^{r}}{k^{r}-k+A_{k}^{r}}\) , here \(A_{k}^{r}=k(k-1)(k-2)\cdots (k-r+1)\) is the number of r permutations from k elements.