Approximating almost-sparse Instances of the Fair Densest
Subgraph in sub-exponential Time

Dorkofikis, Ioannis; Δορκοφίκης, Ιωάννης

dc.contributor.author	Dorkofikis, Ioannis	en
dc.contributor.author	Δορκοφίκης, Ιωάννης	el
dc.date.accessioned	2025-04-04T07:13:00Z
dc.date.available	2025-04-04T07:13:00Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/61616
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.29312
dc.rights	Αναφορά Δημιουργού 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by/3.0/gr/	*
dc.subject	Approximation	en
dc.subject	Exhaustive sampling	en
dc.subject	Randomized rounding	en
dc.subject	Linear programming	en
dc.subject	Fairness	en
dc.subject	Προσέγγιση	el
dc.subject	Εξαντλητική δειγματοληψία	el
dc.subject	Randomized rounding	en
dc.subject	Γραμμικός προγραμματισμός	el
dc.subject	Δικαιοσύνη	el
dc.subject	Υποεκθετικός χρόνος	el
dc.subject	Sub-exponential time	en
dc.title	Approximating almost-sparse Instances of the Fair Densest Subgraph in sub-exponential Time	en
heal.type	bachelorThesis
heal.classification	Algorithms and Complexity	en
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2024-10-29
heal.abstract	This thesis studies the approach introduced in (Arora, Karger, Karpinski, JCSS 99) to approximate dense instances of many important NP-hard problems, including max- imum cut, maximum k-satisfiability and densest k-subgraph, and presents some of its extensions. By dense instances we mean those where the number of constraints (edges) is large relative to the number variables (vertices). The technique is based on the idea of exhaustive sampling: Select a small subset of vertices at random, “guess” their placement in the optimal solution by trying every possible placement and using this information determine where the rest of the vertices should be placed. By applying linear programming techniques in addition to randomized rounding, they develop a PTAS for approximating integer programs where the objective function and the constraints are “dense”, smooth, constant-degree polynomials. The framework is extended in (Fotakis, Lampis, Paschos, STACS 2016), where they use sub-exponential time to provide an (1−ε)-approximation for such polynomial integer programs while relaxing the denseness requirement. They show that increasing the size of the random sample and therefore the running time of the algorithm allows it to handle instances that are a lot less dense, while maintaining an approximation guarantee of (1 − ε). In this work, we show that this extension can be applied to give a sub-exponential (1 − ε)-approximation algorithm for “almost sparse” instances of the fair densest subgraph problem, where we have additional fairness constraints, thus demonstrating the flexibility of this technique.	en
heal.advisorName	Fotakis, Dimitris	en
heal.committeeMemberName	Φωτάκης, Δημήτριος	el
heal.committeeMemberName	Αχλιόπτας, Δημήτριος	el
heal.committeeMemberName	Παγουρτζής, Αριστείδης	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών. Τομέας Τεχνολογίας Πληροφορικής και Υπολογιστών	el
heal.academicPublisherID	ntua
heal.numberOfPages	66 σ.	el
heal.fullTextAvailability	false