Approximation Algorithms for Directed Weighted Spanners (Joint work with Elena Grigorescu and Young-San Lin):
Unification of Spanners and Steiner forests in the directed setting.
Published in APPROX2023.
Multicriteria Spanners -- A New Tool for Network Design (Joint work with Elena Grigorescu and Young-San Lin):
Extension of Spanners where edge lengths are replaced by vector of lengths. Allows encoding of multiple constraints and tracks consumption of multiple resources (such as fuel and time) for the same demand pair.
Established reductions from natural problems such as graph spanners for group steiner distances thereby providing new approximation algorithms for these problems.
(Under submission)
Directed Buy-at-Bulk Spanners (Joint work with Elena Grigorescu and Young-San Lin):
Unification of Weighted spanners and Buy at Bulk Network design (in the directed setting).
Additionally, allows edge lengths to be negative (unexplored even for unit weight spanners in previous literature) as well as rational. Also extends the restricted shortest path problem by allowing edge lengths to be negative.
(Under submission).
Phase Transitions of Diversity in Stochastic Block Model Dynamics (Joint work with Simina Brânzei and Gireeja Ranade):
Published in Allerton 2023.
A study of cops and robbers in oriented graphs (Joint work with Devvrit Khatri, Natasha Komarov, Aaron Krim-Yee, Ben Seamone, Virgelot Virgile, AnQi Xu)
Fractional eternal domination: securely distributing resources across a network (Joint work with Devvrit Khatri, Gary MacGillivray, Aaron Krim-Yee, Ben Seamone, Virgelot Virgile, AnQi Xu)
Accepted in DMGT (Article in press)