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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.03786 |
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| _version_ | 1866908434664783872 |
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| author | Nutov, Zeev Cohen, Reut |
| author_facet | Nutov, Zeev Cohen, Reut |
| contents | In the $k$-Edge Connected Spanning Subgraph ($k$-ECSS) problem we are given a (multi-)graph $G=(V,E)$ with edge costs and an integer $k$, and seek a min-cost $k$-edge-connected spanning subgraph of $G$. The problem admits a $2$-approximation algorithm and no better approximation ratio is known. Recently, Hershkowitz, Klein, and Zenklusen [STOC 24] gave a bicriteria $(1,k-10)$-approximation algorithm that computes a $(k-10)$-edge-connected spanning subgraph of cost at most the optimal value of a standard Cut-LP for $k$-ECSS. We improve the bicriteria approximation to $(1,k-4)$, and also give another non-trivial bicriteria approximation $(3/2,k-2)$. The $k$-Edge-Connected Spanning Multi-subgraph ($k$-ECSM) problem is almost the same as $k$-ECSS, except that any edge can be selected multiple times at the same cost. A $(1,k-p)$ bicriteria approximation for $k$-ECSS w.r.t. Cut-LP implies approximation ratio $1+p/k$ for $k$-ECSM, hence our result also improves the approximation ratio for $k$-ECSM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03786 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bicriteria approximation for $k$-edge-connectivity Nutov, Zeev Cohen, Reut Data Structures and Algorithms In the $k$-Edge Connected Spanning Subgraph ($k$-ECSS) problem we are given a (multi-)graph $G=(V,E)$ with edge costs and an integer $k$, and seek a min-cost $k$-edge-connected spanning subgraph of $G$. The problem admits a $2$-approximation algorithm and no better approximation ratio is known. Recently, Hershkowitz, Klein, and Zenklusen [STOC 24] gave a bicriteria $(1,k-10)$-approximation algorithm that computes a $(k-10)$-edge-connected spanning subgraph of cost at most the optimal value of a standard Cut-LP for $k$-ECSS. We improve the bicriteria approximation to $(1,k-4)$, and also give another non-trivial bicriteria approximation $(3/2,k-2)$. The $k$-Edge-Connected Spanning Multi-subgraph ($k$-ECSM) problem is almost the same as $k$-ECSS, except that any edge can be selected multiple times at the same cost. A $(1,k-p)$ bicriteria approximation for $k$-ECSS w.r.t. Cut-LP implies approximation ratio $1+p/k$ for $k$-ECSM, hence our result also improves the approximation ratio for $k$-ECSM. |
| title | Bicriteria approximation for $k$-edge-connectivity |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2507.03786 |