Hello!
I am a PhD candidate in the University of Michigan’s Industrial
and Operations Engineering department. My research centers
discrete optimization and approximation algorithms. I started my work in Michigan
with developing exact algorithms for the Maximum-Entropy Sampling Problem (MESP), an NP-Hard problem. Motivated by an environmental design problem, the MESP seeks to find the most informative subset of sensors in a sensor network. I have worked on compiling data that we can use as input to test the lower and upper bounds of the model.
My current work focused on stochastic variants of combinatorial optimization problems like the set cover problem and the minimum element problem. My goal is to improve current theoretical guarantees for this combinatorial optimization problem.
My dissertation work covers:
- Maximum-entropy sampling
- Minimum adaptive submodular cover
- Stochastic minimum element
I will
be graduating in December and hope to be joining an institute with a thriving research environment.
When I'm not doing research, I like to be outdoors hiking, climbing or whatever the local environment has to offer.
Featured Publications
H Al-Thani, Y Cui, V Nagarajan
Submitted 2024, Mathematics of Operations Research
We address the minimum cost cover problem of adaptive-submodular functions and introduce a 4(1+lnQ)-approximation algorithm, where Q represents the target value. Additionally, we tackle a more comprehensive objective: minimizing the p-th moment of the coverage cost. Our results demonstrate that our algorithm provides a (p+1)^{p+1}(lnQ +1)^p) approximation guarantee for all p ≥ 1. Adaptive submodularity is a crucial concept in stochastic optimization, relevant to various fields including sensor placement, hypothesis identification, and viral marketing.
Tridiagonal maximum-entropy sampling and tridiagonal masks
H Al-Thani, J Lee
Published 2023, Discrete Applied Mathematics
We present exact solutions to specific cases of the maximum-entropy sampling problem where the covariance matrix is tridiagonal or has a structure induced by a spider graph. We also present a condition where the MESP can be solved exactly for arrowhead matricies, that are generally know to be NP-hard.
Full List of Publications