Approximation Algorithms for Hop Constrained and Buy-at-Bulk Network Design via Hop Constrained Oblivious Routing
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913329269702656 |
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| author | Chekuri, Chandra Jain, Rhea |
| author_facet | Chekuri, Chandra Jain, Rhea |
| contents | We consider two-cost network design models in which edges of the input graph have an associated cost and length. We build upon recent advances in hop-constrained oblivious routing to obtain two sets of results.
We address multicommodity buy-at-bulk network design in the nonuniform setting. Existing poly-logarithmic approximations are based on the junction tree approach [CHKS09,KN11]. We obtain a new polylogarithmic approximation via a natural LP relaxation. This establishes an upper bound on its integrality gap and affirmatively answers an open question raised in [CHKS09]. The rounding is based on recent results in hop-constrained oblivious routing [GHZ21], and this technique yields a polylogarithmic approximation in more general settings such as set connectivity. Our algorithm for buy-at-bulk network design is based on an LP-based reduction to hop constrained network design for which we obtain LP-based bicriteria approximation algorithms.
We also consider a fault-tolerant version of hop constrained network design where one wants to design a low-cost network to guarantee short paths between a given set of source-sink pairs even when k-1 edges can fail. This model has been considered in network design [GL17,GML18,AJL20] but no approximation algorithms were known. We obtain polylogarithmic bicriteria approximation algorithms for the single-source setting for any fixed k. We build upon the single-source algorithm and the junction-tree approach to obtain an approximation algorithm for the multicommodity setting when at most one edge can fail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation Algorithms for Hop Constrained and Buy-at-Bulk Network Design via Hop Constrained Oblivious Routing Chekuri, Chandra Jain, Rhea Data Structures and Algorithms We consider two-cost network design models in which edges of the input graph have an associated cost and length. We build upon recent advances in hop-constrained oblivious routing to obtain two sets of results. We address multicommodity buy-at-bulk network design in the nonuniform setting. Existing poly-logarithmic approximations are based on the junction tree approach [CHKS09,KN11]. We obtain a new polylogarithmic approximation via a natural LP relaxation. This establishes an upper bound on its integrality gap and affirmatively answers an open question raised in [CHKS09]. The rounding is based on recent results in hop-constrained oblivious routing [GHZ21], and this technique yields a polylogarithmic approximation in more general settings such as set connectivity. Our algorithm for buy-at-bulk network design is based on an LP-based reduction to hop constrained network design for which we obtain LP-based bicriteria approximation algorithms. We also consider a fault-tolerant version of hop constrained network design where one wants to design a low-cost network to guarantee short paths between a given set of source-sink pairs even when k-1 edges can fail. This model has been considered in network design [GL17,GML18,AJL20] but no approximation algorithms were known. We obtain polylogarithmic bicriteria approximation algorithms for the single-source setting for any fixed k. We build upon the single-source algorithm and the junction-tree approach to obtain an approximation algorithm for the multicommodity setting when at most one edge can fail. |
| title | Approximation Algorithms for Hop Constrained and Buy-at-Bulk Network Design via Hop Constrained Oblivious Routing |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2404.16725 |