Length-Constrained Network Design in Planar Digraphs | Paper Citation Record

Observation ddd825da-471c-4f09-8d71-f5b9ef9c06bf · outbound

This paper cites Reachability preservers: New extremal bounds and approxi- mation algorithms.SIAM Journal on Computing, 53(2):221–246, 2024.

Length-Constrained Network Design in Planar Digraphs Reachability preservers: New extremal bounds and approxi- mation algorithms.SIAM Journal on Computing, 53(2):221–246, 2024

Reference 1

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Observation 1de1c36c-18e4-4966-9281-72e8ddfa277e · outbound

This paper cites New formulations of the hop-constrained minimum spanning tree problem via Miller-Tucker-Zemlin constraints.European Journal of Operational Research, 212(2):263–276, 2011.

Length-Constrained Network Design in Planar Digraphs New formulations of the hop-constrained minimum spanning tree problem via Miller-Tucker-Zemlin constraints.European Journal of Operational Research, 212(2):263–276, 2011

Reference 2

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Observation 9fb4f927-350d-46c1-b630-dbc73c9e40c0 · outbound

This paper cites Ramos, and Mar- tin Skutella.

Length-Constrained Network Design in Planar Digraphs Ramos, and Mar- tin Skutella

Reference 3

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Observation 6092f559-4e73-400d-b5ef-1a4e1d7b6a02 · outbound

This paper cites Structure and Dynamics of the Globular Cluster Palomar 13.

Length-Constrained Network Design in Planar Digraphs Structure and Dynamics of the Globular Cluster Palomar 13

Reference 4

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Observation 56e4bab3-2682-4351-acb9-b8262f8cd4af · outbound

This paper cites Using a hop-constrained model to generate alternative communication network design.ORSA Journal on Computing, 4(2):192–205, 1992.

Length-Constrained Network Design in Planar Digraphs Using a hop-constrained model to generate alternative communication network design.ORSA Journal on Computing, 4(2):192–205, 1992

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.888971Z

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Observation 02821886-a2be-43ff-80ef-7dab3c9d8193 · outbound

This paper cites Bateni, M.

Length-Constrained Network Design in Planar Digraphs Bateni, M

Reference 6

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Observation 1502bda0-bead-45ef-895b-f5d735f03445 · outbound

This paper cites Approximation algorithms for spanner problems and directed Steiner forest.

Length-Constrained Network Design in Planar Digraphs Approximation algorithms for spanner problems and directed Steiner forest

Reference 7

Resolution: verified exact; doi, observed 2026-08-01T01:41:33.183160Z

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Observation 2fe32cb3-f086-450b-92ad-abc6968d3adf · outbound

This paper cites Near linear time(1 +ϵ)-approximation for restricted shortest paths in undi- rected graphs.

Length-Constrained Network Design in Planar Digraphs Near linear time(1 +ϵ)-approximation for restricted shortest paths in undi- rected graphs

Reference 8

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Observation 454453a4-bb50-453b-a53b-fcb097fe2523 · outbound

This paper cites AnO(nlogn)approximation scheme for Steiner tree in planar graphs.ACM Transactions on Algorithms (TALG), 5(3):1–31, 2009.

Length-Constrained Network Design in Planar Digraphs AnO(nlogn)approximation scheme for Steiner tree in planar graphs.ACM Transactions on Algorithms (TALG), 5(3):1–31, 2009

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.898165Z

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Observation a32466c1-df2f-4141-aa29-553847cc918c · outbound

This paper cites Approximation algorithms for directed Steiner problems.Journal of Algorithms, 33(1):73–91, 1999.

Length-Constrained Network Design in Planar Digraphs Approximation algorithms for directed Steiner problems.Journal of Algorithms, 33(1):73–91, 1999

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.900368Z

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Observation ec4daf32-1780-4214-914c-f81dd84d30f5 · outbound

This paper cites Chekuri, M.

Length-Constrained Network Design in Planar Digraphs Chekuri, M

Reference 11

Resolution: verified exact; doi, observed 2026-08-01T01:41:33.042106Z

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Observation c20c7f91-a5eb-4941-95fe-1a8367d58afc · outbound

This paper cites Set connectivity problems in undirected graphs and the directed steiner network problem.ACM Transactions on Algorithms (TALG), 7(2):1–17, 2011.

Length-Constrained Network Design in Planar Digraphs Set connectivity problems in undirected graphs and the directed steiner network problem.ACM Transactions on Algorithms (TALG), 7(2):1–17, 2011

Reference 12

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Observation be251b21-6e6b-4ce0-8124-79cb656ffadc · outbound

This paper cites Approximation algorithms for hop constrained and buy-at- bulk network design via hop constrained oblivious routing.

Length-Constrained Network Design in Planar Digraphs Approximation algorithms for hop constrained and buy-at- bulk network design via hop constrained oblivious routing

Reference 13

Resolution: verified exact; doi, observed 2026-08-01T01:41:32.756283Z

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Observation 92b3bbb0-9b54-4a9e-b5be-ab5ec638d0d4 · outbound

This paper cites A polylogarithmic approximation for Directed Steiner Forest in planar digraphs.

Length-Constrained Network Design in Planar Digraphs A polylogarithmic approximation for Directed Steiner Forest in planar digraphs

Reference 14

Resolution: verified exact; doi, observed 2026-08-01T01:41:32.549456Z

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Observation 1b7b41aa-1bf1-4c0c-94bf-0831e46a05ff · outbound

This paper cites Node-weighted multicut in planar digraphs.arXiv preprint arXiv:2601.20038, 2026.

Length-Constrained Network Design in Planar Digraphs Node-weighted multicut in planar digraphs.arXiv preprint arXiv:2601.20038, 2026

Reference 15

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Observation 470adc11-98d1-4a68-b095-00d65facba35 · outbound

This paper cites A polylogarithmic approximation for buy-at-bulk network design with protection.

Length-Constrained Network Design in Planar Digraphs A polylogarithmic approximation for buy-at-bulk network design with protection

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.913002Z

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Observation bff0f303-b08d-45ea-9700-77bea249070b · outbound

This paper cites From Directed Steiner Tree to Directed Polymatroid Steiner Tree in Planar Graphs.

Length-Constrained Network Design in Planar Digraphs From Directed Steiner Tree to Directed Polymatroid Steiner Tree in Planar Graphs

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.914901Z

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Observation 516f0af1-af64-4369-9d47-9602b0730322 · outbound

This paper cites A recursive greedy algorithm for walks in directed graphs.

Length-Constrained Network Design in Planar Digraphs A recursive greedy algorithm for walks in directed graphs

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.916884Z

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Observation 9c3c4c17-2212-42e8-bf31-28935ac1b25a · outbound

This paper cites Approximating span- ners and directed steiner forest: Upper and lower bounds.ACM Transactions on Algorithms (TALG), 16(3):1–31, 2020.

Length-Constrained Network Design in Planar Digraphs Approximating span- ners and directed steiner forest: Upper and lower bounds.ACM Transactions on Algorithms (TALG), 16(3):1–31, 2020

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.918835Z

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Observation a2d25338-b88d-4414-9c84-a514be0f0a20 · outbound

This paper cites Bypassing the surface embedding: approximation schemes for network design in minor-free graphs.

Length-Constrained Network Design in Planar Digraphs Bypassing the surface embedding: approximation schemes for network design in minor-free graphs

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.920875Z

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Observation cab2a914-eec0-467c-b40f-16df317d66cc · outbound

This paper cites The 2-hop spanning tree problem.Operations Research Letters, 23(1):21–26, 1998.

Length-Constrained Network Design in Planar Digraphs The 2-hop spanning tree problem.Operations Research Letters, 23(1):21–26, 1998

Reference 21

Resolution: verified exact; doi, observed 2026-08-01T01:41:32.434793Z

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Observation 48f45ba0-cb2e-44d9-9848-ae338625603f · outbound

This paper cites Node-weighted Steiner tree and group Steiner tree in planar graphs.ACM Transactions on Algorithms (TALG), 10(3):1–20,.

Length-Constrained Network Design in Planar Digraphs Node-weighted Steiner tree and group Steiner tree in planar graphs.ACM Transactions on Algorithms (TALG), 10(3):1–20,

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.924854Z

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Observation aaf7fce1-84dd-4244-8e90-96293e30e57f · outbound

This paper cites Label cover instances with large girth and the hardness of approximating basic k-spanner.ACM Trans.

Length-Constrained Network Design in Planar Digraphs Label cover instances with large girth and the hardness of approximating basic k-spanner.ACM Trans

Reference 23

Resolution: verified exact; doi, observed 2026-08-01T01:41:32.304284Z

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Observation 9bd8349a-b97f-49a0-b454-4b959b4db0f0 · outbound

This paper cites Design networks with bounded pairwise distance.

Length-Constrained Network Design in Planar Digraphs Design networks with bounded pairwise distance

Reference 24

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Observation f627391c-8872-49df-b10b-403549cac584 · outbound

This paper cites Improved approximation algorithms for Directed Steiner Forest.Journal of Computer and System Sciences, 78(1):279–292, January.

Length-Constrained Network Design in Planar Digraphs Improved approximation algorithms for Directed Steiner Forest.Journal of Computer and System Sciences, 78(1):279–292, January

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.931172Z

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Observation 5aa23133-d852-48c6-b026-2871aeebb34f · outbound

This paper cites Linear programming hierarchies suffice for directed Steiner tree.

Length-Constrained Network Design in Planar Digraphs Linear programming hierarchies suffice for directed Steiner tree

Reference 27

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Observation 65a12122-9e1e-4214-9332-9525cc3da0ae · outbound

This paper cites A constant-factor approximation for quasi-bipartite directed Steiner tree on minor-free graphs.

Length-Constrained Network Design in Planar Digraphs A constant-factor approximation for quasi-bipartite directed Steiner tree on minor-free graphs

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T01:40:39.939656Z

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Observation d17f3ae3-f68c-47e8-a275-bbd9d3b1278d · outbound

This paper cites AO(logk)-Approximation for Directed Steiner Tree in Planar Graphs.ACM Transactions on Algorithms, 21(4):1–14, 2025.

Length-Constrained Network Design in Planar Digraphs AO(logk)-Approximation for Directed Steiner Tree in Planar Graphs.ACM Transactions on Algorithms, 21(4):1–14, 2025

Reference 29

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Observation aba20104-9a8b-4c55-9cb3-3cecff31a9d9 · outbound

This paper cites Quasi-polynomial algorithms for submodular tree orienteering and directed network design problems.Mathematics of Operations Research, 47(2):1612–1630, 2022.

Length-Constrained Network Design in Planar Digraphs Quasi-polynomial algorithms for submodular tree orienteering and directed network design problems.Mathematics of Operations Research, 47(2):1612–1630, 2022

Reference 31

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Observation b7ba2ce0-f8ec-4ab5-8a95-a4296ad81b32 · outbound

This paper cites Efficient computation of delay-sensitive routes from one source to all destinations.

Length-Constrained Network Design in Planar Digraphs Efficient computation of delay-sensitive routes from one source to all destinations

Reference 32

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Observation 260adb78-cda6-482a-8d93-7639f96fd855 · outbound

This paper cites Preliminary version in Proc.

Length-Constrained Network Design in Planar Digraphs Preliminary version in Proc

Reference 33

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Observation c2ac51a1-180f-41a7-8dc0-c178f24e29d0 · outbound

This paper cites Directed buy-at-bulk spanners.

Length-Constrained Network Design in Planar Digraphs Directed buy-at-bulk spanners

Reference 34

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Observation 300dbe15-e16b-47b8-8aad-69ba2ffbab15 · outbound

This paper cites Ellis Hershkowitz, and Goran Zuzic.

Length-Constrained Network Design in Planar Digraphs Ellis Hershkowitz, and Goran Zuzic

Reference 35

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Observation 0ff56e21-8021-47ec-bc3f-78b2a6d3be69 · outbound

This paper cites Approximating buy-at-bulk and shallow-lightk-steiner trees.Algorithmica, 53:89–103, 2009.

Length-Constrained Network Design in Planar Digraphs Approximating buy-at-bulk and shallow-lightk-steiner trees.Algorithmica, 53:89–103, 2009

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Observation 3d25f582-cabf-408a-8875-feaf84a074e6 · outbound

This paper cites Polylogarithmic inapproximability.

Length-Constrained Network Design in Planar Digraphs Polylogarithmic inapproximability

Reference 37

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Observation 1862b7a2-0c3d-4eae-8a68-6e5f02e52093 · outbound

This paper cites Approximation schemes for the restricted shortest path problem.Mathematics of Operations research, 17(1):36–42, 1992.

Length-Constrained Network Design in Planar Digraphs Approximation schemes for the restricted shortest path problem.Mathematics of Operations research, 17(1):36–42, 1992

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Observation df1c27e5-1871-4be0-b8a7-af271c9f03f5 · outbound

This paper cites Planar length-constrained minimum spanning trees.

Length-Constrained Network Design in Planar Digraphs Planar length-constrained minimum spanning trees

Reference 39

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Observation 30a5866b-ace5-435e-98c8-5e221136c903 · outbound

This paper cites Simple length-constrained minimum spanning trees.

Length-Constrained Network Design in Planar Digraphs Simple length-constrained minimum spanning trees

Reference 40

Resolution: verified exact; doi, observed 2026-08-01T01:41:32.030589Z

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Observation 895cac8f-69ae-4cad-9d0f-71ba77eb7270 · outbound

This paper cites University of Illinois at Urbana-Champaign, 2026.

Length-Constrained Network Design in Planar Digraphs University of Illinois at Urbana-Champaign, 2026

Reference 41

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Observation 6a4a3211-e361-42b2-a0f2-0d23d9b39189 · outbound

This paper cites WH Freeman, 1979.

Length-Constrained Network Design in Planar Digraphs WH Freeman, 1979

Reference 42

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Observation 902ad9be-44c0-466a-8e0e-72bc1d71122a · outbound

This paper cites The shortest route problem with constraints.Journal of Mathematical analysis and applications, 14(2):191–197, 1966.

Length-Constrained Network Design in Planar Digraphs The shortest route problem with constraints.Journal of Mathematical analysis and applications, 14(2):191–197, 1966

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Observation 07ecaada-45bb-4051-9458-6900ac4b8ffd · outbound

This paper cites Approximate hierarchical facility location and applications to the shallow steiner tree and range assignment problems.

Length-Constrained Network Design in Planar Digraphs Approximate hierarchical facility location and applications to the shallow steiner tree and range assignment problems

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Observation bf51c75f-741b-4b71-b23b-3b6e85976737 · outbound

This paper cites Embeddings of planar quasimetrics into directedℓ 1 and polylogarithmic approximation for directed sparsest-cut.

Length-Constrained Network Design in Planar Digraphs Embeddings of planar quasimetrics into directedℓ 1 and polylogarithmic approximation for directed sparsest-cut

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Observation a7b34a5a-542f-4253-adc3-580b563137c3 · outbound

This paper cites Reza Khani and Mohammad R.

Length-Constrained Network Design in Planar Digraphs Reza Khani and Mohammad R

Reference 46

Resolution: verified exact; doi, observed 2026-08-01T01:41:31.942990Z

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Observation 6363a07d-c3e1-4255-9610-84eea15e6212 · outbound

This paper cites Approximating the degree-bounded min- imum diameter spanning tree problem.Algorithmica, 41:117–129, 2005.

Length-Constrained Network Design in Planar Digraphs Approximating the degree-bounded min- imum diameter spanning tree problem.Algorithmica, 41:117–129, 2005

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Observation d38e1fd6-bb65-4839-82d1-721af0076d70 · outbound

This paper cites Approximating some network design problems with node costs.

Length-Constrained Network Design in Planar Digraphs Approximating some network design problems with node costs

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Resolution: verified exact; doi, observed 2026-08-01T01:41:31.840930Z

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Observation 8269fe50-43fd-48ca-bca1-7b8a6f6e622c · outbound

This paper cites Approximating shallow-light trees.

Length-Constrained Network Design in Planar Digraphs Approximating shallow-light trees

Reference 49

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Observation 262e6be1-2617-46a5-88ff-bc7bb19f22c4 · outbound

This paper cites On the integrality gap of directed Steiner tree LPs with relatively integral solutions.arXiv preprint arXiv:2412.10744, 2024.

Length-Constrained Network Design in Planar Digraphs On the integrality gap of directed Steiner tree LPs with relatively integral solutions.arXiv preprint arXiv:2412.10744, 2024

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Observation ba82cad3-9015-4afe-9f14-3a5150231f7b · outbound

This paper cites Polynomial integrality gap of flow LP for directed Steiner tree.

Length-Constrained Network Design in Planar Digraphs Polynomial integrality gap of flow LP for directed Steiner tree

Reference 51

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Observation e37bc868-1adb-4099-91ff-e7d6d601c8f5 · outbound

This paper cites Lipton and Robert Endre Tarjan.

Length-Constrained Network Design in Planar Digraphs Lipton and Robert Endre Tarjan

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Observation 1c2c1da1-a808-4421-8501-1a161f09fc36 · outbound

This paper cites A simple efficient approximation scheme for the restricted shortest path problem.Operations Research Letters, 28(5):213–219, 2001.

Length-Constrained Network Design in Planar Digraphs A simple efficient approximation scheme for the restricted shortest path problem.Operations Research Letters, 28(5):213–219, 2001

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Observation 1b0902a6-6324-4591-8b51-3c40503b9d16 · outbound

This paper cites Bicriteria network design problems.Journal of Algorithms, 28(1):142–171,.

Length-Constrained Network Design in Planar Digraphs Bicriteria network design problems.Journal of Algorithms, 28(1):142–171,

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Observation 138935d0-dadb-455e-b9db-51629e654c99 · outbound

This paper cites New formulations and solution procedures for the hop con- strained network design problem.European Journal of Operational Research, 148(1):126–140,.

Length-Constrained Network Design in Planar Digraphs New formulations and solution procedures for the hop con- strained network design problem.European Journal of Operational Research, 148(1):126–140,

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Observation c39a7505-7098-4750-887c-e3dd098f5390 · outbound

This paper cites Rapidrumorramification: approximatingtheminimumbroadcasttime.

Length-Constrained Network Design in Planar Digraphs Rapidrumorramification: approximatingtheminimumbroadcasttime

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Observation 54053264-daed-407c-ae14-3b547fe20184 · outbound

This paper cites Compact oracles for reachability and approximate distances in planar digraphs.

Length-Constrained Network Design in Planar Digraphs Compact oracles for reachability and approximate distances in planar digraphs

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This paper cites Approximation of pareto optima in multiple-objective, shortest-path prob- lems.Operations research, 35(1):70–79, 1987.

Length-Constrained Network Design in Planar Digraphs Approximation of pareto optima in multiple-objective, shortest-path prob- lems.Operations research, 35(1):70–79, 1987

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Observation 89ebb591-af68-4496-bcf7-ada8f4796e3d · outbound

This paper cites A series of approximation algorithms for the acyclic directed Steiner tree problem.Algorithmica, 18(1):99–110, 1997.

Length-Constrained Network Design in Planar Digraphs A series of approximation algorithms for the acyclic directed Steiner tree problem.Algorithmica, 18(1):99–110, 1997

Reference 60

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Observation 2422aa36-b192-452b-a8dd-0bf9552ff22e · outbound

This paper cites On directed Steiner trees.

Length-Constrained Network Design in Planar Digraphs On directed Steiner trees

Reference 61

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Reference 1998

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Reference 2003

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Observation ebd59fbb-4ba5-4425-a8a8-748b07f756cf · outbound

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Length-Constrained Network Design in Planar Digraphs Unresolved cited work

Reference 2006

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This paper cites Directed Steiner Tree and the Lasserre Hierarchy.

Length-Constrained Network Design in Planar Digraphs Directed Steiner Tree and the Lasserre Hierarchy

Reference 2011

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Reference 2012

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Reference 2023

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