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The Hospital Residents setting models important problems like school choice, assignment of undergraduate students to degree programs, among many others. In this setting, fixed quotas are associated with the programs that limit the number of…
Reallocating resources to get mutually beneficial outcomes is a fundamental problem in various multi-agent settings. While finding an arbitrary Pareto optimal allocation is generally easy, checking whether a particular allocation is Pareto…
The paper discusses diverse interconnected relationships formed within a seemingly unrelated group of students and a conceptually different problem statement. This study uses a Social Network Analysis (SNA) to analyze and map the…
How is the limited capacity of working memory efficiently used to support human linguistic behaviors? In this paper, we propose Strategic Resource Allocation (SRA) as an efficiency principle for memory encoding in sentence processing. The…
In high-stakes scenarios-such as self-harm, legal, or medical queries-LLMs must be both trustworthy and helpful. However, these goals often conflict. We propose priority alignment, a new alignment paradigm that enforces a strict…
Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
This doctoral work focuses on three main problems related to social networks: (1) Orchestrating Network Formation: We consider the problem of orchestrating formation of a social network having a certain given topology that may be desirable…
In a typical school choice application, the students have strict preferences over the schools while the schools have coarse priorities over the students based on their distance and their enrolled siblings. The outcome of a centralized…
This paper has two objectives. One is to give a linear time algorithm that solves the stable roommates problem (i.e., obtains one stable matching) using the stable marriage problem. The idea is that a stable matching of a roommate instance…
The academic job market for new statisticians is highly congested at the interview stage, where departments must rank and select candidates from large applicant pools without credible signals of candidate interest. As a result, interviews…
We study control problems in the context of matching under preferences: We examine how a central authority, called the controller, can manipulate an instance of the Stable Marriage or Stable Roommates problems in order to achieve certain…
We revisit a classical scheduling model to incorporate modern trends in data center networks and cloud services. Addressing some key challenges in the allocation of shared resources to user requests (jobs) in such settings, we consider the…
In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria. Such settings have…
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…
This study addresses the challenge of efficiently assigning locomotives in large freight rail networks, where operational complexity and power imbalances make cost-effective planning difficult. It presents a strategic optimization framework…
Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is a promising technology to achieve full-space coverage. This paper investigates the resource allocation problem in a STAR-RIS-assisted multi-carrier…
The Stable Marriage problem (SM), solved by the famous deferred acceptance algorithm of Gale and Shapley (GS), has many natural generalizations. If we allow ties in preferences, then the problem of finding a maximum stable matching becomes…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley[GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
In the Hospital Residents problem with lower and upper quotas ($HR-Q^U_L$), the goal is to find a stable matching of residents to hospitals where the number of residents matched to a hospital is either between its lower and upper quota or…