{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/129413"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/129413","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Algorithmic aspects of connectivity and density in graphs and hypergraphs","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms","abstract_has_math":false,"creators":["Kulkarni, Shubhang M"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Chandrasekaran, Karthekeyan","Chekuri, Chandra","Har-Peled, Sariel","Bérczi, Kristóf"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-04-24","date_published":"2025-04-24","updated_at":"2026-07-22T22:25:05Z","subjects":["Combinatorial Optimization","Graph Optimization","Hypergraph Optimization","Submodular Functions","Polyhedral Combinatorics","Approximation Algorithms","Linear Programming","Randomized Algorithms","Connectivity Augmentation","Densest Subgraph","Hypergraph Splitting-Off","Feedback Vertex Set"],"languages":["en","eng"],"rights":["Copyright 2025 Shubhang Kulkarni"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/129413","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chandrasekaran, Karthekeyan","Chekuri, Chandra","Har-Peled, Sariel","Bérczi, Kristóf"]},{"key":"dc:creator","label":"Author","values":["Kulkarni, Shubhang M"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-04-24","2025-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Combinatorial Optimization","Graph Optimization","Hypergraph Optimization","Submodular Functions","Polyhedral Combinatorics","Approximation Algorithms","Linear Programming","Randomized Algorithms","Connectivity Augmentation","Densest Subgraph","Hypergraph Splitting-Off","Feedback Vertex Set"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Shubhang Kulkarni"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/129413"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms","The student, Shubhang Kulkarni, accepted the attached license on 2025-04-20 at 11:53.","The student, Shubhang Kulkarni, submitted this Dissertation for approval on 2025-04-21 at 16:17.","This Dissertation was approved for publication on 2025-04-24 at 09:38.","DSpace SAF Submission Ingestion Package generated from Vireo submission #21842 on 2025-10-19 at 18:18:27","This thesis investigates algorithmic problems in combinatorial optimization centered around modifying a given network—via deletion, augmentation, or reconfiguration—to achieve tar- get connectivity or density bounds. We study associated optimization problems on graphs, hypergraphs, and submodular functions. Our main contributions are: • Hypergraph Splitting-off. We introduce a splitting-off operation in hypergraphs and prove an analogue of Mader’s theorem: in every hypergraph, a vertex can be re- moved via splitting-off while preserving all pairwise edge-connectivities. We give a strongly polynomial-time algorithm in weighted hypergraphs, with applications including a constructive characterization of k-hyperedge-connected hypergraphs and an alternate proof of an approximate min-max relation for Steiner rooted-connected orientations. Our framework extends to symmetric skew-supermodular functions. • Hypergraph Connectivity Augmentation. We study augmentation to achieve target pairwise connectivities subject to vertex degree constraints. We give a strongly polynomial time algorithm, improving prior pseudo-polynomial results. Our method extends to generating near-uniform hypergraphs, simultaneously augmenting two hypergraphs, and to covering skew-supermodular functions. Applications include strongly polyno- mial time algorithms for node-to-area and mixed-hypergraph connectivity augmentation. • Graph Density Deletion. We study vertex deletion on graphs where the goal is to delete a minimum-cost subset of vertices so that the densest subgraph has density at most a given target ρ. When ρ ≤ 1, this problem is 2-approximable. In contrast, we show logarithmic hardness of approximation for all fixed integers ρ > 1. We also study a generalization to monotone supermodular functions, show approximation equivalence to Submodular Set Cover, and design bicriteria approximation algorithms. • Feedback Vertex Set (FVS) and Pseudoforest Deletion Set (PFDS). We undertake a polyhedral study of FVS and PFDS, special cases of graph density deletion for appropriate ρ ≤ 1. Both problems are 2-approximable, but lacked polynomial-time solvable LP relaxations with matching approximation guarantees. We establish the first such LP formulations for both problems. For PFDS, we resolve a question of Bodlaender, Ono and Otachi by exhibiting an extreme point property of an associated polytope."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Algorithmic aspects of connectivity and density in graphs and hypergraphs"]}]}],"canonical_facts":{"dc:contributor":["Chandrasekaran, Karthekeyan","Chekuri, Chandra","Har-Peled, Sariel","Bérczi, Kristóf"],"dc:creator":["Kulkarni, Shubhang M"],"dc:date":["2025-04-24","2025-05"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms","The student, Shubhang Kulkarni, accepted the attached license on 2025-04-20 at 11:53.","The student, Shubhang Kulkarni, submitted this Dissertation for approval on 2025-04-21 at 16:17.","This Dissertation was approved for publication on 2025-04-24 at 09:38.","DSpace SAF Submission Ingestion Package generated from Vireo submission #21842 on 2025-10-19 at 18:18:27","This thesis investigates algorithmic problems in combinatorial optimization centered around modifying a given network—via deletion, augmentation, or reconfiguration—to achieve tar- get connectivity or density bounds. We study associated optimization problems on graphs, hypergraphs, and submodular functions. Our main contributions are: • Hypergraph Splitting-off. We introduce a splitting-off operation in hypergraphs and prove an analogue of Mader’s theorem: in every hypergraph, a vertex can be re- moved via splitting-off while preserving all pairwise edge-connectivities. We give a strongly polynomial-time algorithm in weighted hypergraphs, with applications including a constructive characterization of k-hyperedge-connected hypergraphs and an alternate proof of an approximate min-max relation for Steiner rooted-connected orientations. Our framework extends to symmetric skew-supermodular functions. • Hypergraph Connectivity Augmentation. We study augmentation to achieve target pairwise connectivities subject to vertex degree constraints. We give a strongly polynomial time algorithm, improving prior pseudo-polynomial results. Our method extends to generating near-uniform hypergraphs, simultaneously augmenting two hypergraphs, and to covering skew-supermodular functions. Applications include strongly polyno- mial time algorithms for node-to-area and mixed-hypergraph connectivity augmentation. • Graph Density Deletion. We study vertex deletion on graphs where the goal is to delete a minimum-cost subset of vertices so that the densest subgraph has density at most a given target ρ. When ρ ≤ 1, this problem is 2-approximable. In contrast, we show logarithmic hardness of approximation for all fixed integers ρ > 1. We also study a generalization to monotone supermodular functions, show approximation equivalence to Submodular Set Cover, and design bicriteria approximation algorithms. • Feedback Vertex Set (FVS) and Pseudoforest Deletion Set (PFDS). We undertake a polyhedral study of FVS and PFDS, special cases of graph density deletion for appropriate ρ ≤ 1. Both problems are 2-approximable, but lacked polynomial-time solvable LP relaxations with matching approximation guarantees. We establish the first such LP formulations for both problems. For PFDS, we resolve a question of Bodlaender, Ono and Otachi by exhibiting an extreme point property of an associated polytope."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/129413"],"dc:language":["en","eng"],"dc:rights":["Copyright 2025 Shubhang Kulkarni"],"dc:subject":["Combinatorial Optimization","Graph Optimization","Hypergraph Optimization","Submodular Functions","Polyhedral Combinatorics","Approximation Algorithms","Linear Programming","Randomized Algorithms","Connectivity Augmentation","Densest Subgraph","Hypergraph Splitting-Off","Feedback Vertex Set"],"dc:title":["Algorithmic aspects of connectivity and density in graphs and hypergraphs"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:05Z"}