Title:
Dual algorithms for the densest subgraph problem

dc.contributor.advisor Peng, Richard
dc.contributor.author Sawlani, Saurabh Sunil Sunil
dc.contributor.committeeMember Randall, Dana
dc.contributor.committeeMember Vigoda, Eric
dc.contributor.committeeMember Yu, Xingxing
dc.contributor.committeeMember Tsourakakis, Charalampos E.
dc.contributor.department Computer Science
dc.date.accessioned 2020-09-08T12:44:06Z
dc.date.available 2020-09-08T12:44:06Z
dc.date.created 2020-08
dc.date.issued 2020-05-19
dc.date.submitted August 2020
dc.date.updated 2020-09-08T12:44:06Z
dc.description.abstract Dense subgraph discovery is an important primitive for many real-world graph mining applications. The dissertation tackles the densest subgraph problem via its dual linear programming formulation. Particularly, our contributions in this thesis are the following: (i) We give a faster width-dependent algorithm to solve mixed packing and covering LPs, a class of problems that is fundamental to combinatorial optimization in computer science and operations research (the dual of the densest subgraph problem is an instance of this class of linear programs) . Our work utilizes the framework of area convexity introduced by Sherman [STOC `17] to obtain accelerated rates of convergence. (ii) We devise an iterative algorithm for the densest subgraph problem which naturally generalizes Charikar's greedy algorithm. Our algorithm draws insights from the iterative approaches from convex optimization, and also exploits the dual interpretation of the densest subgraph problem. We have empirical evidence that our algorithm is much more robust against the structural heterogeneities in real-world datasets, and converges to the optimal subgraph density even when the simple greedy algorithm fails. (iii) Lastly, we design the first fully-dynamic algorithm which maintains a $(1-\epsilon)$ approximate densest subgraph in worst-case $\text{poly}(\log n, \epsilon^{-1})$ time per update. Our result improves upon the previous best approximation factor of $(1/4 - \epsilon)$ for fully dynamic densest subgraph.
dc.description.degree Ph.D.
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/63582
dc.language.iso en_US
dc.publisher Georgia Institute of Technology
dc.subject Graph algorithms
dc.subject Densest subgraph
dc.subject Dynamic algorithms
dc.subject Mixed packing and covering linear programs
dc.subject Greedy
dc.title Dual algorithms for the densest subgraph problem
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Peng, Richard
local.contributor.corporatename College of Computing
local.contributor.corporatename School of Computer Science
relation.isAdvisorOfPublication 3d73f7e1-6610-4b66-9c3a-906e35a0b6de
relation.isOrgUnitOfPublication c8892b3c-8db6-4b7b-a33a-1b67f7db2021
relation.isOrgUnitOfPublication 6b42174a-e0e1-40e3-a581-47bed0470a1e
thesis.degree.level Doctoral
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