Maintaining the Giant Component in Networks With Edge Weighted Augmentation Given Causal Failures Article Swipe
Zuyuan Zhang
,
Sridhar Radhakrishnan
,
Kash Barker
,
Andrés D. González
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1109/access.2024.3462851
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1109/access.2024.3462851
Understanding the relationship between various nodes of a network is critical for building a robust and resilient network. Studying and understanding the causes of network failures is vital to prevent electric grid blackouts, mitigate supply chain failures, and keep transportation systems functional, among others. Failure of one or more nodes may cause other nodes in the network to fail as well, that is, failures are causal. In general, these failure relationships extend beyond the immediate neighborhood of failed nodes. When any of the causal failures are applied (the nodes of the causal failures are removed), the network could be disconnected. One can add edges to the original network (augmentation problem) in such a way that the network remains connected after applying each of the causal failures, or the largest connected component in the disconnected network is at least a given specified size (-giant component), where n is the number of nodes in the original network. By choosing this size, we guarantee that the network is active for a large population of entities represented by the nodes in the giant component. More formally, we consider the network augmentation problem when faced with causal failures as follows. Given a network , its complement with a cost function and the causality set , find a subset of with a minimum total cost such that the network maintains at least one -giant component when each causal failure in is applied to the augmented graph. We prove the NP-hardness of this problem and present a mixed integer linear programming model to provide the exact solution to the problem. Furthermore, we design a heuristic algorithm by checking the connected components when applying each causality. Finally, experiments are conducted on synthetic Erdős-Rényi networks, and we demonstrate the efficacy and efficiency of the heuristic algorithm relative to the mixed-integer linear programming model.
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1109/access.2024.3462851
- OA Status
- gold
- Cited By
- 3
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4402568564
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4402568564Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1109/access.2024.3462851Digital Object Identifier
- Title
-
Maintaining the Giant Component in Networks With Edge Weighted Augmentation Given Causal FailuresWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-01-01Full publication date if available
- Authors
-
Zuyuan Zhang, Sridhar Radhakrishnan, Kash Barker, Andrés D. GonzálezList of authors in order
- Landing page
-
https://doi.org/10.1109/access.2024.3462851Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.1109/access.2024.3462851Direct OA link when available
- Concepts
-
Component (thermodynamics), Computer science, Enhanced Data Rates for GSM Evolution, Artificial intelligence, Thermodynamics, PhysicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
3Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 3Per-year citation counts (last 5 years)
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4402568564 |
|---|---|
| doi | https://doi.org/10.1109/access.2024.3462851 |
| ids.doi | https://doi.org/10.1109/access.2024.3462851 |
| ids.openalex | https://openalex.org/W4402568564 |
| fwci | 2.5105983 |
| type | article |
| title | Maintaining the Giant Component in Networks With Edge Weighted Augmentation Given Causal Failures |
| biblio.issue | |
| biblio.volume | 12 |
| biblio.last_page | 136598 |
| biblio.first_page | 136588 |
| topics[0].id | https://openalex.org/T12879 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9023000001907349 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1705 |
| topics[0].subfield.display_name | Computer Networks and Communications |
| topics[0].display_name | Distributed Sensor Networks and Detection Algorithms |
| is_xpac | False |
| apc_list.value | 1850 |
| apc_list.currency | USD |
| apc_list.value_usd | 1850 |
| apc_paid.value | 1850 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 1850 |
| concepts[0].id | https://openalex.org/C168167062 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7143260836601257 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1117970 |
| concepts[0].display_name | Component (thermodynamics) |
| concepts[1].id | https://openalex.org/C41008148 |
| concepts[1].level | 0 |
| concepts[1].score | 0.5941498279571533 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[1].display_name | Computer science |
| concepts[2].id | https://openalex.org/C162307627 |
| concepts[2].level | 2 |
| concepts[2].score | 0.5546904802322388 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q204833 |
| concepts[2].display_name | Enhanced Data Rates for GSM Evolution |
| concepts[3].id | https://openalex.org/C154945302 |
| concepts[3].level | 1 |
| concepts[3].score | 0.23352399468421936 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[3].display_name | Artificial intelligence |
| concepts[4].id | https://openalex.org/C97355855 |
| concepts[4].level | 1 |
| concepts[4].score | 0.0 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q11473 |
| concepts[4].display_name | Thermodynamics |
| concepts[5].id | https://openalex.org/C121332964 |
| concepts[5].level | 0 |
| concepts[5].score | 0.0 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[5].display_name | Physics |
| keywords[0].id | https://openalex.org/keywords/component |
| keywords[0].score | 0.7143260836601257 |
| keywords[0].display_name | Component (thermodynamics) |
| keywords[1].id | https://openalex.org/keywords/computer-science |
| keywords[1].score | 0.5941498279571533 |
| keywords[1].display_name | Computer science |
| keywords[2].id | https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution |
| keywords[2].score | 0.5546904802322388 |
| keywords[2].display_name | Enhanced Data Rates for GSM Evolution |
| keywords[3].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[3].score | 0.23352399468421936 |
| keywords[3].display_name | Artificial intelligence |
| language | en |
| locations[0].id | doi:10.1109/access.2024.3462851 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S2485537415 |
| locations[0].source.issn | 2169-3536 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2169-3536 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | IEEE Access |
| locations[0].source.host_organization | https://openalex.org/P4310319808 |
| locations[0].source.host_organization_name | Institute of Electrical and Electronics Engineers |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310319808 |
| locations[0].source.host_organization_lineage_names | Institute of Electrical and Electronics Engineers |
| locations[0].license | |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | IEEE Access |
| locations[0].landing_page_url | https://doi.org/10.1109/access.2024.3462851 |
| locations[1].id | pmh:oai:doaj.org/article:b21b6c7d92094a1eaec332097b094f86 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306401280 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | DOAJ (DOAJ: Directory of Open Access Journals) |
| locations[1].source.host_organization | |
| locations[1].source.host_organization_name | |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | article |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | IEEE Access, Vol 12, Pp 136588-136598 (2024) |
| locations[1].landing_page_url | https://doaj.org/article/b21b6c7d92094a1eaec332097b094f86 |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5004425960 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-5795-9771 |
| authorships[0].author.display_name | Zuyuan Zhang |
| authorships[0].countries | US |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I8692664 |
| authorships[0].affiliations[0].raw_affiliation_string | School of Computer Science, University of Oklahoma, Norman, Oklahoma, USA |
| authorships[0].institutions[0].id | https://openalex.org/I8692664 |
| authorships[0].institutions[0].ror | https://ror.org/02aqsxs83 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I8692664 |
| authorships[0].institutions[0].country_code | US |
| authorships[0].institutions[0].display_name | University of Oklahoma |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Zuyuan Zhang |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | School of Computer Science, University of Oklahoma, Norman, Oklahoma, USA |
| authorships[1].author.id | https://openalex.org/A5101878770 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-0327-8134 |
| authorships[1].author.display_name | Sridhar Radhakrishnan |
| authorships[1].countries | US |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I8692664 |
| authorships[1].affiliations[0].raw_affiliation_string | School of Computer Science, University of Oklahoma, Norman, Oklahoma, USA |
| authorships[1].institutions[0].id | https://openalex.org/I8692664 |
| authorships[1].institutions[0].ror | https://ror.org/02aqsxs83 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I8692664 |
| authorships[1].institutions[0].country_code | US |
| authorships[1].institutions[0].display_name | University of Oklahoma |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Sridhar Radhakrishnan |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | School of Computer Science, University of Oklahoma, Norman, Oklahoma, USA |
| authorships[2].author.id | https://openalex.org/A5064032094 |
| authorships[2].author.orcid | https://orcid.org/0000-0002-0142-1558 |
| authorships[2].author.display_name | Kash Barker |
| authorships[2].countries | US |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I8692664 |
| authorships[2].affiliations[0].raw_affiliation_string | School of Industrial and Systems Engineering, University of Oklahoma, Norman, Oklahoma, USA |
| authorships[2].institutions[0].id | https://openalex.org/I8692664 |
| authorships[2].institutions[0].ror | https://ror.org/02aqsxs83 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I8692664 |
| authorships[2].institutions[0].country_code | US |
| authorships[2].institutions[0].display_name | University of Oklahoma |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Kash Barker |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | School of Industrial and Systems Engineering, University of Oklahoma, Norman, Oklahoma, USA |
| authorships[3].author.id | https://openalex.org/A5082373340 |
| authorships[3].author.orcid | https://orcid.org/0000-0003-0613-5224 |
| authorships[3].author.display_name | Andrés D. González |
| authorships[3].countries | US |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I8692664 |
| authorships[3].affiliations[0].raw_affiliation_string | School of Industrial and Systems Engineering, University of Oklahoma, Norman, Oklahoma, USA |
| authorships[3].institutions[0].id | https://openalex.org/I8692664 |
| authorships[3].institutions[0].ror | https://ror.org/02aqsxs83 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I8692664 |
| authorships[3].institutions[0].country_code | US |
| authorships[3].institutions[0].display_name | University of Oklahoma |
| authorships[3].author_position | last |
| authorships[3].raw_author_name | Andrés D. González |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | School of Industrial and Systems Engineering, University of Oklahoma, Norman, Oklahoma, USA |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.1109/access.2024.3462851 |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Maintaining the Giant Component in Networks With Edge Weighted Augmentation Given Causal Failures |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T12879 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9023000001907349 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1705 |
| primary_topic.subfield.display_name | Computer Networks and Communications |
| primary_topic.display_name | Distributed Sensor Networks and Detection Algorithms |
| related_works | https://openalex.org/W4391375266, https://openalex.org/W2748952813, https://openalex.org/W2390279801, https://openalex.org/W2358668433, https://openalex.org/W4396701345, https://openalex.org/W2376932109, https://openalex.org/W2001405890, https://openalex.org/W4396696052, https://openalex.org/W2382290278, https://openalex.org/W4395014643 |
| cited_by_count | 3 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 3 |
| locations_count | 2 |
| best_oa_location.id | doi:10.1109/access.2024.3462851 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S2485537415 |
| best_oa_location.source.issn | 2169-3536 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2169-3536 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | IEEE Access |
| best_oa_location.source.host_organization | https://openalex.org/P4310319808 |
| best_oa_location.source.host_organization_name | Institute of Electrical and Electronics Engineers |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310319808 |
| best_oa_location.source.host_organization_lineage_names | Institute of Electrical and Electronics Engineers |
| best_oa_location.license | |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | IEEE Access |
| best_oa_location.landing_page_url | https://doi.org/10.1109/access.2024.3462851 |
| primary_location.id | doi:10.1109/access.2024.3462851 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S2485537415 |
| primary_location.source.issn | 2169-3536 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2169-3536 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | IEEE Access |
| primary_location.source.host_organization | https://openalex.org/P4310319808 |
| primary_location.source.host_organization_name | Institute of Electrical and Electronics Engineers |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310319808 |
| primary_location.source.host_organization_lineage_names | Institute of Electrical and Electronics Engineers |
| primary_location.license | |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | IEEE Access |
| primary_location.landing_page_url | https://doi.org/10.1109/access.2024.3462851 |
| publication_date | 2024-01-01 |
| publication_year | 2024 |
| referenced_works_count | 0 |
| abstract_inverted_index.$ | 151, 268 |
| abstract_inverted_index.a | 7, 13, 112, 138, 177, 206, 223, 244, 253, 296, 313 |
| abstract_inverted_index.n | 155 |
| abstract_inverted_index.By | 165 |
| abstract_inverted_index.In | 66 |
| abstract_inverted_index.We | 287 |
| abstract_inverted_index.as | 59, 203 |
| abstract_inverted_index.at | 136, 262 |
| abstract_inverted_index.be | 98 |
| abstract_inverted_index.by | 183, 316 |
| abstract_inverted_index.in | 54, 110, 131, 161, 186, 275 |
| abstract_inverted_index.is | 9, 26, 135, 156, 174, 281 |
| abstract_inverted_index.n$ | 146 |
| abstract_inverted_index.of | 6, 23, 45, 76, 81, 89, 122, 159, 180, 246, 291, 340 |
| abstract_inverted_index.on | 329 |
| abstract_inverted_index.or | 47, 126 |
| abstract_inverted_index.to | 28, 57, 104, 283, 302, 307, 345 |
| abstract_inverted_index.we | 169, 192, 311, 334 |
| abstract_inverted_index.E)$ | 211 |
| abstract_inverted_index.One | 100 |
| abstract_inverted_index.add | 102 |
| abstract_inverted_index.and | 15, 19, 37, 234, 294, 333, 338 |
| abstract_inverted_index.any | 80 |
| abstract_inverted_index.are | 64, 85, 93, 327 |
| abstract_inverted_index.can | 101 |
| abstract_inverted_index.for | 11, 176 |
| abstract_inverted_index.is, | 62 |
| abstract_inverted_index.its | 213 |
| abstract_inverted_index.may | 50 |
| abstract_inverted_index.one | 46, 264 |
| abstract_inverted_index.set | 237 |
| abstract_inverted_index.the | 1, 21, 55, 73, 82, 90, 95, 105, 115, 123, 127, 132, 157, 162, 172, 184, 187, 194, 235, 259, 284, 289, 304, 308, 318, 336, 341, 346 |
| abstract_inverted_index.way | 113 |
| abstract_inverted_index.{E} | 230 |
| abstract_inverted_index.(the | 87 |
| abstract_inverted_index.More | 190 |
| abstract_inverted_index.When | 79 |
| abstract_inverted_index.\bar | 219, 229 |
| abstract_inverted_index.cost | 224, 256 |
| abstract_inverted_index.each | 121, 272, 323 |
| abstract_inverted_index.fail | 58 |
| abstract_inverted_index.find | 243 |
| abstract_inverted_index.grid | 31 |
| abstract_inverted_index.keep | 38 |
| abstract_inverted_index.more | 48 |
| abstract_inverted_index.size | 141 |
| abstract_inverted_index.such | 111, 257 |
| abstract_inverted_index.that | 61, 114, 171, 258 |
| abstract_inverted_index.this | 167, 292 |
| abstract_inverted_index.when | 198, 271, 321 |
| abstract_inverted_index.with | 200, 222, 252 |
| abstract_inverted_index.{C}$ | 241, 279 |
| abstract_inverted_index.{E}$ | 250 |
| abstract_inverted_index.Given | 205 |
| abstract_inverted_index.after | 119 |
| abstract_inverted_index.among | 42 |
| abstract_inverted_index.cause | 51 |
| abstract_inverted_index.chain | 35 |
| abstract_inverted_index.could | 97 |
| abstract_inverted_index.edges | 103 |
| abstract_inverted_index.exact | 305 |
| abstract_inverted_index.faced | 199 |
| abstract_inverted_index.giant | 188 |
| abstract_inverted_index.given | 139 |
| abstract_inverted_index.large | 178 |
| abstract_inverted_index.least | 137, 263 |
| abstract_inverted_index.mixed | 297 |
| abstract_inverted_index.model | 301 |
| abstract_inverted_index.nodes | 5, 49, 53, 88, 160, 185 |
| abstract_inverted_index.other | 52 |
| abstract_inverted_index.prove | 288 |
| abstract_inverted_index.size, | 168 |
| abstract_inverted_index.these | 68 |
| abstract_inverted_index.total | 255 |
| abstract_inverted_index.vital | 27 |
| abstract_inverted_index.well, | 60 |
| abstract_inverted_index.where | 154 |
| abstract_inverted_index.{E})$ | 220 |
| abstract_inverted_index.R^{+}$ | 232 |
| abstract_inverted_index.\times | 145 |
| abstract_inverted_index.active | 175 |
| abstract_inverted_index.beyond | 72 |
| abstract_inverted_index.causal | 83, 91, 124, 201, 273 |
| abstract_inverted_index.causes | 22 |
| abstract_inverted_index.design | 312 |
| abstract_inverted_index.extend | 71 |
| abstract_inverted_index.failed | 77 |
| abstract_inverted_index.graph. | 286 |
| abstract_inverted_index.linear | 299, 348 |
| abstract_inverted_index.model. | 350 |
| abstract_inverted_index.nodes. | 78 |
| abstract_inverted_index.number | 158 |
| abstract_inverted_index.robust | 14 |
| abstract_inverted_index.subset | 245 |
| abstract_inverted_index.supply | 34 |
| abstract_inverted_index.Failure | 44 |
| abstract_inverted_index.applied | 86, 282 |
| abstract_inverted_index.between | 3 |
| abstract_inverted_index.causal. | 65 |
| abstract_inverted_index.failure | 69, 274 |
| abstract_inverted_index.integer | 298 |
| abstract_inverted_index.largest | 128 |
| abstract_inverted_index.minimum | 254 |
| abstract_inverted_index.network | 8, 24, 56, 96, 107, 116, 134, 173, 195, 207, 260 |
| abstract_inverted_index.others. | 43 |
| abstract_inverted_index.present | 295 |
| abstract_inverted_index.prevent | 29 |
| abstract_inverted_index.problem | 197, 293 |
| abstract_inverted_index.provide | 303 |
| abstract_inverted_index.remains | 117 |
| abstract_inverted_index.systems | 40 |
| abstract_inverted_index.various | 4 |
| abstract_inverted_index.{G}=(V, | 218 |
| abstract_inverted_index.Finally, | 325 |
| abstract_inverted_index.Studying | 18 |
| abstract_inverted_index.applying | 120, 322 |
| abstract_inverted_index.building | 12 |
| abstract_inverted_index.checking | 317 |
| abstract_inverted_index.choosing | 166 |
| abstract_inverted_index.consider | 193 |
| abstract_inverted_index.critical | 10 |
| abstract_inverted_index.efficacy | 337 |
| abstract_inverted_index.electric | 30 |
| abstract_inverted_index.entities | 181 |
| abstract_inverted_index.failures | 25, 63, 84, 92, 202 |
| abstract_inverted_index.follows. | 204 |
| abstract_inverted_index.function | 225 |
| abstract_inverted_index.general, | 67 |
| abstract_inverted_index.mitigate | 33 |
| abstract_inverted_index.network. | 17, 164 |
| abstract_inverted_index.original | 106, 163 |
| abstract_inverted_index.problem) | 109 |
| abstract_inverted_index.problem. | 309 |
| abstract_inverted_index.relative | 344 |
| abstract_inverted_index.solution | 306 |
| abstract_inverted_index.<tex-math | 143, 149, 209, 216, 227, 239, 248, 266, 277 |
| abstract_inverted_index.algorithm | 315, 343 |
| abstract_inverted_index.augmented | 285 |
| abstract_inverted_index.causality | 236 |
| abstract_inverted_index.component | 130, 270 |
| abstract_inverted_index.conducted | 328 |
| abstract_inverted_index.connected | 118, 129, 319 |
| abstract_inverted_index.failures, | 36, 125 |
| abstract_inverted_index.formally, | 191 |
| abstract_inverted_index.guarantee | 170 |
| abstract_inverted_index.heuristic | 314, 342 |
| abstract_inverted_index.immediate | 74 |
| abstract_inverted_index.maintains | 261 |
| abstract_inverted_index.networks, | 332 |
| abstract_inverted_index.removed), | 94 |
| abstract_inverted_index.resilient | 16 |
| abstract_inverted_index.specified | 140 |
| abstract_inverted_index.synthetic | 330 |
| abstract_inverted_index.blackouts, | 32 |
| abstract_inverted_index.causality. | 324 |
| abstract_inverted_index.complement | 214 |
| abstract_inverted_index.component. | 189 |
| abstract_inverted_index.components | 320 |
| abstract_inverted_index.efficiency | 339 |
| abstract_inverted_index.population | 179 |
| abstract_inverted_index.NP-hardness | 290 |
| abstract_inverted_index.\rightarrow | 231 |
| abstract_inverted_index.component), | 153 |
| abstract_inverted_index.demonstrate | 335 |
| abstract_inverted_index.experiments | 326 |
| abstract_inverted_index.functional, | 41 |
| abstract_inverted_index.programming | 300, 349 |
| abstract_inverted_index.represented | 182 |
| abstract_inverted_index.Furthermore, | 310 |
| abstract_inverted_index.augmentation | 196 |
| abstract_inverted_index.disconnected | 133 |
| abstract_inverted_index.neighborhood | 75 |
| abstract_inverted_index.relationship | 2 |
| abstract_inverted_index.(augmentation | 108 |
| abstract_inverted_index.Understanding | 0 |
| abstract_inverted_index.disconnected. | 99 |
| abstract_inverted_index.mixed-integer | 347 |
| abstract_inverted_index.relationships | 70 |
| abstract_inverted_index.understanding | 20 |
| abstract_inverted_index.transportation | 39 |
| abstract_inverted_index.<inline-formula> | 142, 208, 215, 226, 238, 247, 265, 276 |
| abstract_inverted_index.(<inline-formula> | 148 |
| abstract_inverted_index.notation="LaTeX">$c: | 228 |
| abstract_inverted_index.notation="LaTeX">$\bar | 217, 249 |
| abstract_inverted_index.notation="LaTeX">$G=(V, | 210 |
| abstract_inverted_index.notation="LaTeX">$\alpha | 144, 150, 267 |
| abstract_inverted_index.Erdős-Rényi | 331 |
| abstract_inverted_index.notation="LaTeX">$\mathcal | 240, 278 |
| abstract_inverted_index.</tex-math></inline-formula> | 147, 221, 233, 251, 280 |
| abstract_inverted_index.</tex-math></inline-formula>, | 212, 242 |
| abstract_inverted_index.</tex-math></inline-formula>-giant | 152, 269 |
| cited_by_percentile_year.max | 97 |
| cited_by_percentile_year.min | 96 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile.value | 0.83663788 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |