Related papers: Ranking Sets of Objects: The Complexity of Avoidin…
We formulate the problem of fair and efficient completion of indivisible goods, defined as follows: Given a partial allocation of indivisible goods among agents, does there exist an allocation of the remaining goods (i.e., a completion)…
In problems involving the allocation of a single non-disposable commodity, we study rules defined on a general domain of preferences requiring only that each preference exhibit a unique global maximum. Our focus is on rules that satisfy a…
Participatory budgeting (PB) has attracted much attention in recent times due to its wide applicability in social choice settings. In this paper, we consider indivisible PB which involves allocating an available, limited budget to a set of…
Finding interesting patterns is a challenging task in data mining. Constraint based mining is a well-known approach to this, and one for which constraint programming has been shown to be a well-suited and generic framework. Dominance…
We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…
Various tasks in decision making and decision support systems require selecting a preferred subset of a given set of items. Here we focus on problems where the individual items are described using a set of characterizing attributes, and a…
Learning to rank -- producing a ranked list of items specific to a query and with respect to a set of supervisory items -- is a problem of general interest. The setting we consider is one in which no analytic description of what constitutes…
We study several decision problems for counter systems with guards defined by convex polyhedra and updates defined by affine transformations. In general, the reachability problem is undecidable for such systems. Decidability can be achieved…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
There are many applications in which it is desirable to order rather than classify instances. Here we consider the problem of learning how to order instances given feedback in the form of preference judgments, i.e., statements to the effect…
Existing observational approaches for learning human preferences, such as inverse reinforcement learning, usually make strong assumptions about the observability of the human's environment. However, in reality, people make many important…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
Given an order, a commutative ring whose additive group is free of finite rank, a natural computational question is whether a fixed univariate polynomial $f \in \mathbb{Z}[X]$ has a root in this ring. In this paper, we show that 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…
Ranking over sets arise when users choose between groups of items. For example, a group may be of those movies deemed $5$ stars to them, or a customized tour package. It turns out, to model this data type properly, we need to investigate…
Given a set U of alternatives, a choice (correspondence) on U is a contractive map c defined on a family Omega of nonempty subsets of U. Semantically, a choice c associates to each menu A in Omega a nonempty subset c(A) of A comprising all…
In a \emph{separability problem}, we are given two sets $K$ and $L$ from a class $\mathcal{C}$, and we want to decide whether there exists a set $S$ from a class $\mathcal{S}$ such that $K\subseteq S$ and $S\cap L=\emptyset$. In this case,…
Classification is a ubiquitous and fundamental problem in artificial intelligence and machine learning, with extensive efforts dedicated to developing more powerful classifiers and larger datasets. However, the classification task is…
Many set selection and ranking algorithms have recently been enhanced with diversity constraints that aim to explicitly increase representation of historically disadvantaged populations, or to improve the overall representativeness of the…
This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…