Node-Weighted Multicut in Planar Digraphs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911403724505088 |
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| author | Chekuri, Chandra Jain, Rhea |
| author_facet | Chekuri, Chandra Jain, Rhea |
| contents | Kawarabayashi and Sidiropoulos [KS22] obtained an $O(\log^2 n)$-approximation algorithm for Multicut in planar digraphs via a natural LP relaxation, which also establishes a corresponding upper bound on the multicommodity flow-cut gap. Their result is in contrast to a lower bound of $\tildeΩ(n^{1/7})$ on the flow-cut gap for general digraphs due to Chuzhoy and Khanna [CK09]. We extend the algorithm and analysis in [KS22] to the node-weighted Multicut problem. Unlike in general digraphs, node-weighted problems cannot be reduced to edge-weighted problems in a black box fashion due to the planarity restriction. We use the node-weighted problem as a vehicle to accomplish two additional goals: (i) to obtain a deterministic algorithm (the algorithm in [KS22] is randomized), and (ii) to simplify and clarify some aspects of the algorithm and analysis from [KS22]. The Multicut result, via a standard technique, implies an approximation for the Nonuniform Sparsest Cut problem with an additional logarithmic factor loss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20038 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Node-Weighted Multicut in Planar Digraphs Chekuri, Chandra Jain, Rhea Data Structures and Algorithms Kawarabayashi and Sidiropoulos [KS22] obtained an $O(\log^2 n)$-approximation algorithm for Multicut in planar digraphs via a natural LP relaxation, which also establishes a corresponding upper bound on the multicommodity flow-cut gap. Their result is in contrast to a lower bound of $\tildeΩ(n^{1/7})$ on the flow-cut gap for general digraphs due to Chuzhoy and Khanna [CK09]. We extend the algorithm and analysis in [KS22] to the node-weighted Multicut problem. Unlike in general digraphs, node-weighted problems cannot be reduced to edge-weighted problems in a black box fashion due to the planarity restriction. We use the node-weighted problem as a vehicle to accomplish two additional goals: (i) to obtain a deterministic algorithm (the algorithm in [KS22] is randomized), and (ii) to simplify and clarify some aspects of the algorithm and analysis from [KS22]. The Multicut result, via a standard technique, implies an approximation for the Nonuniform Sparsest Cut problem with an additional logarithmic factor loss. |
| title | Node-Weighted Multicut in Planar Digraphs |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2601.20038 |