Dynamic framework for edge-connectivity maintenance of simple graphs
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911497906552832 |
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| author | Wrobel, Blazej |
| author_facet | Wrobel, Blazej |
| contents | We present a framework for dynamically maintaining $k$-edge-connectivity of an undirected simple graph $G$ under edge insertions and deletions, where $k$ is a fixed constant. After an edge insertion, the algorithm identifies and removes a distinct redundant edge to maintain sparsity, in $O(k \log n)$ amortized time. After an edge deletion that reduces $λ(G)$ below $k$, the algorithm restores $k$-edge-connectivity by adding at most two new edges (excluding the deleted edge), in $O(k^{3/2} n^{3/2})$ time. The insertion procedure combines Nagamochi-Ibaraki sparse certificates with Link-Cut Trees; the deletion procedure uses a single maximum-flow computation on the sparsified graph. Throughout all updates, the graph is maintained with $O(kn)$ edges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20137 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamic framework for edge-connectivity maintenance of simple graphs Wrobel, Blazej Data Structures and Algorithms We present a framework for dynamically maintaining $k$-edge-connectivity of an undirected simple graph $G$ under edge insertions and deletions, where $k$ is a fixed constant. After an edge insertion, the algorithm identifies and removes a distinct redundant edge to maintain sparsity, in $O(k \log n)$ amortized time. After an edge deletion that reduces $λ(G)$ below $k$, the algorithm restores $k$-edge-connectivity by adding at most two new edges (excluding the deleted edge), in $O(k^{3/2} n^{3/2})$ time. The insertion procedure combines Nagamochi-Ibaraki sparse certificates with Link-Cut Trees; the deletion procedure uses a single maximum-flow computation on the sparsified graph. Throughout all updates, the graph is maintained with $O(kn)$ edges. |
| title | Dynamic framework for edge-connectivity maintenance of simple graphs |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2601.20137 |