{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hypersteiner-computing-heuristic-hyperbolic","title":"HyperSteiner: Computing Heuristic Hyperbolic Steiner Minimal Trees","arxiv_id":"2409.05671","date":"2024-09-09","proceeding":null,"authors":["Alejandro García-Castellanos","Aniss Aiman Medbouhi","Giovanni Luca Marchetti","Erik J. Bekkers","Danica Kragic"],"abstract":"We propose HyperSteiner -- an efficient heuristic algorithm for computing Steiner minimal trees in the hyperbolic space. HyperSteiner extends the Euclidean Smith-Lee-Liebman algorithm, which is grounded in a divide-and-conquer approach involving the Delaunay triangulation. The central idea is rephrasing Steiner tree problems with three terminals as a system of equations in the Klein-Beltrami model. Motivated by the fact that hyperbolic geometry is well-suited for representing hierarchies, we explore applications to hierarchy discovery in data. Results show that HyperSteiner infers more realistic hierarchies than the Minimum Spanning Tree and is more scalable to large datasets than Neighbor Joining.","url_abs":"https://arxiv.org/abs/2409.05671v2","url_pdf":"https://arxiv.org/pdf/2409.05671v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"hypersteiner-computing-heuristic-hyperbolic","repo_url":"https://github.com/AGarciaCast/HyperSteiner","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2409.05671","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2409.05671"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/AGarciaCast/HyperSteiner","reach":{"status":"ok"}}],"summary":{"ran":21,"unverified":6},"by_repo_kind":{"official":{"samples":27,"ran":21,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":27,"samples":[{"code_sha256_prefix":"954c202d6b0fe97b","entry":"cyclic","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/families.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/families.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"954c202d6b0fe97b"}},{"code_sha256_prefix":"e43d27c3eb0c1557","entry":"dobldobl_decomposition","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/factor.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/factor.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e43d27c3eb0c1557"}},{"code_sha256_prefix":"a8ddaba7ccdddc6d","entry":"get_homotopy_continuation_parameter","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/curves.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/curves.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a8ddaba7ccdddc6d"}},{"code_sha256_prefix":"f43e5279466e16fe","entry":"is_binomial_system","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/maps.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/maps.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f43e5279466e16fe"}},{"code_sha256_prefix":"eeec159cc1ce04a8","entry":"katsura","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/families.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/families.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"eeec159cc1ce04a8"}},{"code_sha256_prefix":"42d94d4c14e24ef1","entry":"katsura_variable","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/families.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/families.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"42d94d4c14e24ef1"}},{"code_sha256_prefix":"625200130b01c7b3","entry":"monomial_map_solutions","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/maps.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/maps.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"625200130b01c7b3"}},{"code_sha256_prefix":"ddf347d940841e9c","entry":"monomial_map_strings","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/maps.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/maps.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"ddf347d940841e9c"}},{"code_sha256_prefix":"9d7b36bfe0f48679","entry":"pols2str","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/dashboard.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/dashboard.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"9d7b36bfe0f48679"}},{"code_sha256_prefix":"37588128ca3becf8","entry":"read_df","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"src/formatResults.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/src/formatResults.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"37588128ca3becf8"}},{"code_sha256_prefix":"7214614be87b67d0","entry":"rearrange_table_convergence","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"src/formatResults.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/src/formatResults.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"7214614be87b67d0"}},{"code_sha256_prefix":"cac42c93a429afe9","entry":"set_homotopy_continuation_gamma","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/curves.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/curves.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"cac42c93a429afe9"}},{"code_sha256_prefix":"6ffe22dbee50aff7","entry":"set_homotopy_continuation_parameter","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/curves.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/curves.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"6ffe22dbee50aff7"}},{"code_sha256_prefix":"3daa7490336ec7ed","entry":"standard_decomposition","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/factor.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/factor.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"3daa7490336ec7ed"}},{"code_sha256_prefix":"6c73d0170ce6c1ea","entry":"standard_double_cascade_step","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/cascades.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/cascades.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"6c73d0170ce6c1ea"}},{"code_sha256_prefix":"3e8aaddb96805230","entry":"standard_start_diagonal_cascade","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/diagonal.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/diagonal.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"3e8aaddb96805230"}},{"code_sha256_prefix":"a7458611a06a8e25","entry":"store_dobldobl_system","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/interface.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/interface.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a7458611a06a8e25"}},{"code_sha256_prefix":"ef679e28d346014b","entry":"store_standard_system","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/interface.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/interface.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"ef679e28d346014b"}},{"code_sha256_prefix":"51a8b9c200b428a6","entry":"str2pols","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/dashboard.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/dashboard.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"51a8b9c200b428a6"}},{"code_sha256_prefix":"176a052754981496","entry":"top_diagonal_dimension","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/diagonal.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/diagonal.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"176a052754981496"}},{"code_sha256_prefix":"e9d419fceb672af6","entry":"windowsize","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/dashboard.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/dashboard.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e9d419fceb672af6"}},{"code_sha256_prefix":"a2417efb27571910","entry":"dobldobl_start_diagonal_cascade","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/diagonal.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/diagonal.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a2417efb27571910"}},{"code_sha256_prefix":"4961d58c3e8dc12f","entry":"double_double_cascade_step","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/cascades.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/cascades.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"4961d58c3e8dc12f"}},{"code_sha256_prefix":"d21615f5c56b415c","entry":"load_standard_tableau","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/interface.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/interface.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"d21615f5c56b415c"}},{"code_sha256_prefix":"d825b08f1e0f4c09","entry":"quad_double_cascade_step","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/cascades.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/cascades.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"d825b08f1e0f4c09"}},{"code_sha256_prefix":"1e9f6cb339057a8c","entry":"quaddobl_decomposition","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"phcpy/factor.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/phcpy/factor.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"1e9f6cb339057a8c"}},{"code_sha256_prefix":"6edb563b9f10ecf7","entry":"rearrange_table_scalability","repo":"AGarciaCast/HyperSteiner","repo_kind":"official","path":"src/formatResults.py","file_url":"https://github.com/AGarciaCast/HyperSteiner/blob/HEAD/src/formatResults.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"6edb563b9f10ecf7"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}