An Approximate Solution to the Minimum Vertex Cover Problem: The Hvala Algorithm Article Swipe
The Minimum Vertex Cover (MVC) problem is a fundamental NP-complete problem in graph theory that seeks the smallest set of vertices covering all edges in an undirected graph G = (V, E). This paper presents the find_vertex_cover algorithm, an innovative approximation method that transforms the problem to maximum degree-1 instances via auxiliary vertices. The algorithm computes solutions using weighted dominating sets and vertex covers on reduced graphs, enhanced by ensemble heuristics including maximum-degree greedy and minimum-to-minimum strategies. Our approach guarantees an approximation ratio strictly less than √2 ≈ 1.414, which would contradict known hardness results unless P = NP. This theoretical implication represents a significant advancement beyond classical approximation bounds. The algorithm operates in O(m log n) time for n vertices and m edges, employing component-wise processing and linear-space reductions for efficiency. Implemented in Python as the Hvala package, it demonstrates excellent performance on sparse and scale-free networks, with profound implications for complexity theory. The achievement of a sub-√2 approximation ratio, if validated, would resolve the P versus NP problem in the affirmative. This work enables near-optimal solutions for applications in network design, scheduling, and bioinformatics while challenging fundamental assumptions in computational complexity.
Related Topics
Concepts
Vertex cover
Approximation algorithm
Mathematics
Heuristics
Feedback vertex set
Greedy algorithm
Combinatorics
Vertex (graph theory)
Algorithm
Set cover problem
Edge cover
Running time
Independent set
Dominating set
Time complexity
Maximum cut
Undirected graph
Discrete mathematics
Graph
Computational complexity theory
Parameterized complexity
Efficient algorithm
Cover (algebra)
Binary logarithm
Graph theory
Set (abstract data type)
Steiner tree problem
Graph algorithms
Neighbourhood (mathematics)
Random graph
Theory of computation
Combinatorial optimization
Metadata
- Type
- article
- Landing Page
- https://doi.org/10.20944/preprints202506.0875.v7
- https://www.preprints.org/frontend/manuscript/08a487d6df033d369bcf7853aabfeebd/download_pub
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7106033577
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W7106033577Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.20944/preprints202506.0875.v7Digital Object Identifier
- Title
-
An Approximate Solution to the Minimum Vertex Cover Problem: The Hvala AlgorithmWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-11-18Full publication date if available
- Authors
-
Frank VegaList of authors in order
- Landing page
-
https://doi.org/10.20944/preprints202506.0875.v7Publisher landing page
- PDF URL
-
https://www.preprints.org/frontend/manuscript/08a487d6df033d369bcf7853aabfeebd/download_pubDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://www.preprints.org/frontend/manuscript/08a487d6df033d369bcf7853aabfeebd/download_pubDirect OA link when available
- Concepts
-
Vertex cover, Approximation algorithm, Mathematics, Heuristics, Feedback vertex set, Greedy algorithm, Combinatorics, Vertex (graph theory), Algorithm, Set cover problem, Edge cover, Running time, Independent set, Dominating set, Time complexity, Maximum cut, Undirected graph, Discrete mathematics, Graph, Computational complexity theory, Parameterized complexity, Efficient algorithm, Cover (algebra), Binary logarithm, Graph theory, Set (abstract data type), Steiner tree problem, Graph algorithms, Neighbourhood (mathematics), Random graph, Theory of computation, Combinatorial optimizationTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
Full payload
| id | https://openalex.org/W7106033577 |
|---|---|
| doi | https://doi.org/10.20944/preprints202506.0875.v7 |
| ids.doi | https://doi.org/10.20944/preprints202506.0875.v7 |
| ids.openalex | https://openalex.org/W7106033577 |
| fwci | 0.0 |
| type | article |
| title | An Approximate Solution to the Minimum Vertex Cover Problem: The Hvala Algorithm |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10720 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.3272014856338501 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1703 |
| topics[0].subfield.display_name | Computational Theory and Mathematics |
| topics[0].display_name | Complexity and Algorithms in Graphs |
| topics[1].id | https://openalex.org/T10374 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.2839870750904083 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1703 |
| topics[1].subfield.display_name | Computational Theory and Mathematics |
| topics[1].display_name | Advanced Graph Theory Research |
| topics[2].id | https://openalex.org/T10829 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.053789179772138596 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1705 |
| topics[2].subfield.display_name | Computer Networks and Communications |
| topics[2].display_name | Interconnection Networks and Systems |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C40687702 |
| concepts[0].level | 3 |
| concepts[0].score | 0.759167492389679 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q11515519 |
| concepts[0].display_name | Vertex cover |
| concepts[1].id | https://openalex.org/C148764684 |
| concepts[1].level | 2 |
| concepts[1].score | 0.7118273973464966 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q621751 |
| concepts[1].display_name | Approximation algorithm |
| concepts[2].id | https://openalex.org/C33923547 |
| concepts[2].level | 0 |
| concepts[2].score | 0.6243419051170349 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[2].display_name | Mathematics |
| concepts[3].id | https://openalex.org/C127705205 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5622179508209229 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q5748245 |
| concepts[3].display_name | Heuristics |
| concepts[4].id | https://openalex.org/C28723256 |
| concepts[4].level | 4 |
| concepts[4].score | 0.5102773308753967 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q1400918 |
| concepts[4].display_name | Feedback vertex set |
| concepts[5].id | https://openalex.org/C51823790 |
| concepts[5].level | 2 |
| concepts[5].score | 0.4996373653411865 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q504353 |
| concepts[5].display_name | Greedy algorithm |
| concepts[6].id | https://openalex.org/C114614502 |
| concepts[6].level | 1 |
| concepts[6].score | 0.48815661668777466 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[6].display_name | Combinatorics |
| concepts[7].id | https://openalex.org/C80899671 |
| concepts[7].level | 3 |
| concepts[7].score | 0.4852496385574341 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q1304193 |
| concepts[7].display_name | Vertex (graph theory) |
| concepts[8].id | https://openalex.org/C11413529 |
| concepts[8].level | 1 |
| concepts[8].score | 0.4722656011581421 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[8].display_name | Algorithm |
| concepts[9].id | https://openalex.org/C100808899 |
| concepts[9].level | 3 |
| concepts[9].score | 0.46907010674476624 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q1192100 |
| concepts[9].display_name | Set cover problem |
| concepts[10].id | https://openalex.org/C17762858 |
| concepts[10].level | 3 |
| concepts[10].score | 0.4473927319049835 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q594001 |
| concepts[10].display_name | Edge cover |
| concepts[11].id | https://openalex.org/C3017489831 |
| concepts[11].level | 2 |
| concepts[11].score | 0.4413744807243347 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q2393193 |
| concepts[11].display_name | Running time |
| concepts[12].id | https://openalex.org/C122818955 |
| concepts[12].level | 3 |
| concepts[12].score | 0.43289485573768616 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q1060343 |
| concepts[12].display_name | Independent set |
| concepts[13].id | https://openalex.org/C146661039 |
| concepts[13].level | 4 |
| concepts[13].score | 0.4238440692424774 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q2915204 |
| concepts[13].display_name | Dominating set |
| concepts[14].id | https://openalex.org/C311688 |
| concepts[14].level | 2 |
| concepts[14].score | 0.41525357961654663 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q2393193 |
| concepts[14].display_name | Time complexity |
| concepts[15].id | https://openalex.org/C165526019 |
| concepts[15].level | 3 |
| concepts[15].score | 0.4088992178440094 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q942557 |
| concepts[15].display_name | Maximum cut |
| concepts[16].id | https://openalex.org/C3018234147 |
| concepts[16].level | 3 |
| concepts[16].score | 0.40080758929252625 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q141488 |
| concepts[16].display_name | Undirected graph |
| concepts[17].id | https://openalex.org/C118615104 |
| concepts[17].level | 1 |
| concepts[17].score | 0.3906058967113495 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q121416 |
| concepts[17].display_name | Discrete mathematics |
| concepts[18].id | https://openalex.org/C132525143 |
| concepts[18].level | 2 |
| concepts[18].score | 0.3756040334701538 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q141488 |
| concepts[18].display_name | Graph |
| concepts[19].id | https://openalex.org/C179799912 |
| concepts[19].level | 2 |
| concepts[19].score | 0.3662263751029968 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q205084 |
| concepts[19].display_name | Computational complexity theory |
| concepts[20].id | https://openalex.org/C165464430 |
| concepts[20].level | 2 |
| concepts[20].score | 0.35282760858535767 |
| concepts[20].wikidata | https://www.wikidata.org/wiki/Q1570441 |
| concepts[20].display_name | Parameterized complexity |
| concepts[21].id | https://openalex.org/C3018263672 |
| concepts[21].level | 2 |
| concepts[21].score | 0.34798893332481384 |
| concepts[21].wikidata | https://www.wikidata.org/wiki/Q1296251 |
| concepts[21].display_name | Efficient algorithm |
| concepts[22].id | https://openalex.org/C2780428219 |
| concepts[22].level | 2 |
| concepts[22].score | 0.33820822834968567 |
| concepts[22].wikidata | https://www.wikidata.org/wiki/Q16952335 |
| concepts[22].display_name | Cover (algebra) |
| concepts[23].id | https://openalex.org/C63553672 |
| concepts[23].level | 2 |
| concepts[23].score | 0.3312261998653412 |
| concepts[23].wikidata | https://www.wikidata.org/wiki/Q581168 |
| concepts[23].display_name | Binary logarithm |
| concepts[24].id | https://openalex.org/C88230418 |
| concepts[24].level | 2 |
| concepts[24].score | 0.32672926783561707 |
| concepts[24].wikidata | https://www.wikidata.org/wiki/Q131476 |
| concepts[24].display_name | Graph theory |
| concepts[25].id | https://openalex.org/C177264268 |
| concepts[25].level | 2 |
| concepts[25].score | 0.31228846311569214 |
| concepts[25].wikidata | https://www.wikidata.org/wiki/Q1514741 |
| concepts[25].display_name | Set (abstract data type) |
| concepts[26].id | https://openalex.org/C76220878 |
| concepts[26].level | 2 |
| concepts[26].score | 0.30229783058166504 |
| concepts[26].wikidata | https://www.wikidata.org/wiki/Q1764144 |
| concepts[26].display_name | Steiner tree problem |
| concepts[27].id | https://openalex.org/C2986651925 |
| concepts[27].level | 3 |
| concepts[27].score | 0.284892201423645 |
| concepts[27].wikidata | https://www.wikidata.org/wiki/Q1514868 |
| concepts[27].display_name | Graph algorithms |
| concepts[28].id | https://openalex.org/C161677786 |
| concepts[28].level | 2 |
| concepts[28].score | 0.27912208437919617 |
| concepts[28].wikidata | https://www.wikidata.org/wiki/Q2478475 |
| concepts[28].display_name | Neighbourhood (mathematics) |
| concepts[29].id | https://openalex.org/C47458327 |
| concepts[29].level | 3 |
| concepts[29].score | 0.2669509947299957 |
| concepts[29].wikidata | https://www.wikidata.org/wiki/Q910404 |
| concepts[29].display_name | Random graph |
| concepts[30].id | https://openalex.org/C24858836 |
| concepts[30].level | 2 |
| concepts[30].score | 0.25982666015625 |
| concepts[30].wikidata | https://www.wikidata.org/wiki/Q844718 |
| concepts[30].display_name | Theory of computation |
| concepts[31].id | https://openalex.org/C52692508 |
| concepts[31].level | 2 |
| concepts[31].score | 0.25002017617225647 |
| concepts[31].wikidata | https://www.wikidata.org/wiki/Q1333872 |
| concepts[31].display_name | Combinatorial optimization |
| keywords[0].id | https://openalex.org/keywords/vertex-cover |
| keywords[0].score | 0.759167492389679 |
| keywords[0].display_name | Vertex cover |
| keywords[1].id | https://openalex.org/keywords/approximation-algorithm |
| keywords[1].score | 0.7118273973464966 |
| keywords[1].display_name | Approximation algorithm |
| keywords[2].id | https://openalex.org/keywords/heuristics |
| keywords[2].score | 0.5622179508209229 |
| keywords[2].display_name | Heuristics |
| keywords[3].id | https://openalex.org/keywords/feedback-vertex-set |
| keywords[3].score | 0.5102773308753967 |
| keywords[3].display_name | Feedback vertex set |
| keywords[4].id | https://openalex.org/keywords/greedy-algorithm |
| keywords[4].score | 0.4996373653411865 |
| keywords[4].display_name | Greedy algorithm |
| keywords[5].id | https://openalex.org/keywords/vertex |
| keywords[5].score | 0.4852496385574341 |
| keywords[5].display_name | Vertex (graph theory) |
| keywords[6].id | https://openalex.org/keywords/set-cover-problem |
| keywords[6].score | 0.46907010674476624 |
| keywords[6].display_name | Set cover problem |
| keywords[7].id | https://openalex.org/keywords/edge-cover |
| keywords[7].score | 0.4473927319049835 |
| keywords[7].display_name | Edge cover |
| keywords[8].id | https://openalex.org/keywords/running-time |
| keywords[8].score | 0.4413744807243347 |
| keywords[8].display_name | Running time |
| keywords[9].id | https://openalex.org/keywords/independent-set |
| keywords[9].score | 0.43289485573768616 |
| keywords[9].display_name | Independent set |
| language | |
| locations[0].id | doi:10.20944/preprints202506.0875.v7 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S6309402219 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Preprints.org |
| locations[0].source.host_organization | |
| locations[0].source.host_organization_name | |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310310987 |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://www.preprints.org/frontend/manuscript/08a487d6df033d369bcf7853aabfeebd/download_pub |
| locations[0].version | acceptedVersion |
| locations[0].raw_type | posted-content |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | https://doi.org/10.20944/preprints202506.0875.v7 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A2465859367 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-8210-4126 |
| authorships[0].author.display_name | Frank Vega |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Frank Vega |
| authorships[0].is_corresponding | True |
| has_content.pdf | True |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://www.preprints.org/frontend/manuscript/08a487d6df033d369bcf7853aabfeebd/download_pub |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-11-19T00:00:00 |
| display_name | An Approximate Solution to the Minimum Vertex Cover Problem: The Hvala Algorithm |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-19T23:39:43.309859 |
| primary_topic.id | https://openalex.org/T10720 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.3272014856338501 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1703 |
| primary_topic.subfield.display_name | Computational Theory and Mathematics |
| primary_topic.display_name | Complexity and Algorithms in Graphs |
| cited_by_count | 0 |
| locations_count | 1 |
| best_oa_location.id | doi:10.20944/preprints202506.0875.v7 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S6309402219 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Preprints.org |
| best_oa_location.source.host_organization | |
| best_oa_location.source.host_organization_name | |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310310987 |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://www.preprints.org/frontend/manuscript/08a487d6df033d369bcf7853aabfeebd/download_pub |
| best_oa_location.version | acceptedVersion |
| best_oa_location.raw_type | posted-content |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | https://doi.org/10.20944/preprints202506.0875.v7 |
| primary_location.id | doi:10.20944/preprints202506.0875.v7 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S6309402219 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Preprints.org |
| primary_location.source.host_organization | |
| primary_location.source.host_organization_name | |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310310987 |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://www.preprints.org/frontend/manuscript/08a487d6df033d369bcf7853aabfeebd/download_pub |
| primary_location.version | acceptedVersion |
| primary_location.raw_type | posted-content |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | https://doi.org/10.20944/preprints202506.0875.v7 |
| publication_date | 2025-11-18 |
| publication_year | 2025 |
| referenced_works_count | 0 |
| abstract_inverted_index.= | 29, 97 |
| abstract_inverted_index.G | 28 |
| abstract_inverted_index.P | 96, 166 |
| abstract_inverted_index.a | 7, 103, 157 |
| abstract_inverted_index.m | 122 |
| abstract_inverted_index.n | 119 |
| abstract_inverted_index.NP | 168 |
| abstract_inverted_index.an | 25, 38, 80 |
| abstract_inverted_index.as | 135 |
| abstract_inverted_index.by | 68 |
| abstract_inverted_index.if | 161 |
| abstract_inverted_index.in | 11, 24, 113, 133, 170, 180, 190 |
| abstract_inverted_index.is | 6 |
| abstract_inverted_index.it | 139 |
| abstract_inverted_index.n) | 116 |
| abstract_inverted_index.of | 19, 156 |
| abstract_inverted_index.on | 64, 143 |
| abstract_inverted_index.to | 46 |
| abstract_inverted_index.(V, | 30 |
| abstract_inverted_index.E). | 31 |
| abstract_inverted_index.NP. | 98 |
| abstract_inverted_index.O(m | 114 |
| abstract_inverted_index.Our | 77 |
| abstract_inverted_index.The | 0, 53, 110, 154 |
| abstract_inverted_index.all | 22 |
| abstract_inverted_index.and | 61, 74, 121, 127, 145, 184 |
| abstract_inverted_index.for | 118, 130, 151, 178 |
| abstract_inverted_index.log | 115 |
| abstract_inverted_index.set | 18 |
| abstract_inverted_index.the | 16, 35, 44, 136, 165, 171 |
| abstract_inverted_index.via | 50 |
| abstract_inverted_index.≈ | 87 |
| abstract_inverted_index.This | 32, 99, 173 |
| abstract_inverted_index.less | 84 |
| abstract_inverted_index.sets | 60 |
| abstract_inverted_index.than | 85 |
| abstract_inverted_index.that | 14, 42 |
| abstract_inverted_index.time | 117 |
| abstract_inverted_index.with | 148 |
| abstract_inverted_index.work | 174 |
| abstract_inverted_index.√2 | 86 |
| abstract_inverted_index.(MVC) | 4 |
| abstract_inverted_index.Cover | 3 |
| abstract_inverted_index.Hvala | 137 |
| abstract_inverted_index.edges | 23 |
| abstract_inverted_index.graph | 12, 27 |
| abstract_inverted_index.known | 92 |
| abstract_inverted_index.paper | 33 |
| abstract_inverted_index.ratio | 82 |
| abstract_inverted_index.seeks | 15 |
| abstract_inverted_index.using | 57 |
| abstract_inverted_index.which | 89 |
| abstract_inverted_index.while | 186 |
| abstract_inverted_index.would | 90, 163 |
| abstract_inverted_index.1.414, | 88 |
| abstract_inverted_index.Python | 134 |
| abstract_inverted_index.Vertex | 2 |
| abstract_inverted_index.beyond | 106 |
| abstract_inverted_index.covers | 63 |
| abstract_inverted_index.edges, | 123 |
| abstract_inverted_index.greedy | 73 |
| abstract_inverted_index.method | 41 |
| abstract_inverted_index.ratio, | 160 |
| abstract_inverted_index.sparse | 144 |
| abstract_inverted_index.theory | 13 |
| abstract_inverted_index.unless | 95 |
| abstract_inverted_index.versus | 167 |
| abstract_inverted_index.vertex | 62 |
| abstract_inverted_index.Minimum | 1 |
| abstract_inverted_index.bounds. | 109 |
| abstract_inverted_index.design, | 182 |
| abstract_inverted_index.enables | 175 |
| abstract_inverted_index.graphs, | 66 |
| abstract_inverted_index.maximum | 47 |
| abstract_inverted_index.network | 181 |
| abstract_inverted_index.problem | 5, 10, 45, 169 |
| abstract_inverted_index.reduced | 65 |
| abstract_inverted_index.resolve | 164 |
| abstract_inverted_index.results | 94 |
| abstract_inverted_index.theory. | 153 |
| abstract_inverted_index.approach | 78 |
| abstract_inverted_index.computes | 55 |
| abstract_inverted_index.covering | 21 |
| abstract_inverted_index.degree-1 | 48 |
| abstract_inverted_index.enhanced | 67 |
| abstract_inverted_index.ensemble | 69 |
| abstract_inverted_index.hardness | 93 |
| abstract_inverted_index.operates | 112 |
| abstract_inverted_index.package, | 138 |
| abstract_inverted_index.presents | 34 |
| abstract_inverted_index.profound | 149 |
| abstract_inverted_index.smallest | 17 |
| abstract_inverted_index.strictly | 83 |
| abstract_inverted_index.sub-√2 | 158 |
| abstract_inverted_index.vertices | 20, 120 |
| abstract_inverted_index.weighted | 58 |
| abstract_inverted_index.algorithm | 54, 111 |
| abstract_inverted_index.auxiliary | 51 |
| abstract_inverted_index.classical | 107 |
| abstract_inverted_index.employing | 124 |
| abstract_inverted_index.excellent | 141 |
| abstract_inverted_index.including | 71 |
| abstract_inverted_index.instances | 49 |
| abstract_inverted_index.networks, | 147 |
| abstract_inverted_index.solutions | 56, 177 |
| abstract_inverted_index.vertices. | 52 |
| abstract_inverted_index.algorithm, | 37 |
| abstract_inverted_index.complexity | 152 |
| abstract_inverted_index.contradict | 91 |
| abstract_inverted_index.dominating | 59 |
| abstract_inverted_index.guarantees | 79 |
| abstract_inverted_index.heuristics | 70 |
| abstract_inverted_index.innovative | 39 |
| abstract_inverted_index.processing | 126 |
| abstract_inverted_index.reductions | 129 |
| abstract_inverted_index.represents | 102 |
| abstract_inverted_index.scale-free | 146 |
| abstract_inverted_index.transforms | 43 |
| abstract_inverted_index.undirected | 26 |
| abstract_inverted_index.validated, | 162 |
| abstract_inverted_index.Implemented | 132 |
| abstract_inverted_index.NP-complete | 9 |
| abstract_inverted_index.achievement | 155 |
| abstract_inverted_index.advancement | 105 |
| abstract_inverted_index.assumptions | 189 |
| abstract_inverted_index.challenging | 187 |
| abstract_inverted_index.complexity. | 192 |
| abstract_inverted_index.efficiency. | 131 |
| abstract_inverted_index.fundamental | 8, 188 |
| abstract_inverted_index.implication | 101 |
| abstract_inverted_index.performance | 142 |
| abstract_inverted_index.scheduling, | 183 |
| abstract_inverted_index.significant | 104 |
| abstract_inverted_index.strategies. | 76 |
| abstract_inverted_index.theoretical | 100 |
| abstract_inverted_index.affirmative. | 172 |
| abstract_inverted_index.applications | 179 |
| abstract_inverted_index.demonstrates | 140 |
| abstract_inverted_index.implications | 150 |
| abstract_inverted_index.linear-space | 128 |
| abstract_inverted_index.near-optimal | 176 |
| abstract_inverted_index.approximation | 40, 81, 108, 159 |
| abstract_inverted_index.computational | 191 |
| abstract_inverted_index.bioinformatics | 185 |
| abstract_inverted_index.component-wise | 125 |
| abstract_inverted_index.maximum-degree | 72 |
| abstract_inverted_index.find_vertex_cover | 36 |
| abstract_inverted_index.minimum-to-minimum | 75 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile.value | 0.84260432 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |