Related papers: Structural Complexities of Matching Mechanisms
The difficulty of an entity matching task depends on a combination of multiple factors such as the amount of corner-case pairs, the fraction of entities in the test set that have not been seen during training, and the size of the…
Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening of the hierarchical models into an equation system for analysis. However, the…
Decomposition and abstraction is an essential component of computational thinking, yet it is not always emphasized in introductory programming courses. In addition, as generative AI further reduces the focus on syntax and increases the…
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic…
Centralized assignment markets have historically relied on Deferred-Acceptance (DA) algorithms, which do not incorporate multiple objectives into the assignment. In this work, we propose an optimization-based many-to-one assignment…
Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach…
We study the classical probabilistic assignment problem, where finitely many indivisible objects are to be probabilistically or proportionally assigned among an equal number of agents. Each agent has an initial deterministic endowment and a…
Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient…
We study dynamic matching in an infinite-horizon stochastic market. While all agents are potentially compatible with each other, some are hard-to-match and others are easy-to-match. Agents prefer to be matched as soon as possible and…
One-sided matching problems with ordinal preferences, such as hostel room allocation, are commonly solved using the Top Trading Cycles (TTC) mechanism, which guarantees Pareto-optimal (PO) outcomes. However, TTC does not yield a unique…
Two-sided matching markets, environments in which two disjoint groups of agents seek to partner with one another, arise in several contexts. In static, centralized markets where agents know their preferences, standard algorithms can yield a…
In this paper, we propose a comprehensive study of second-order consistencies (i.e., consistencies identifying inconsistent pairs of values) for constraint satisfaction. We build a full picture of the relationships existing between four…
In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…
Fixed-parameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixed-parameter algorithms are appealing…
In many matching markets, one side "applies" to the other, and these applications are often expensive and time-consuming (e.g. students applying to college). It is tempting to think that making the application process easier should benefit…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
In many two-sided markets, the parties to be matched have incomplete information about their characteristics. We consider the settings where the parties engaged are extremely patient and are interested in long-term partnerships. Hence, once…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
The successive and the amendment procedures have been widely employed in parliamentary and legislative decision making and have undergone extensive study in the literature from various perspectives. However, investigating them through the…
In school choice, policymakers consolidate a district's objectives for a school into a priority ordering over students. They then face a trade-off between respecting these priorities and assigning students to more-preferred schools.…