Related papers: Ranking Sets of Objects: The Complexity of Avoidin…
The nondeterministic advice complexity of the P-selective sets is known to be exactly linear. Regarding the deterministic advice complexity of the P-selective sets--i.e., the amount of Karp--Lipton advice needed for polynomial-time machines…
We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings…
Object ranking is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects, which are typically represented as feature vectors, the goal is to learn a ranking…
We provide the first evidence for the inherent difficulty of finding complex sets with optimal proof systems. For this, we construct oracles $O_1$ and $O_2$ with the following properties, where $\mathrm{RE}$ denotes the class of recursively…
Algorithmic decidability is established for two order-theoretic properties of downward closed subsets defined by finitely many obstructions in two infinite posets. The properties under consideration are: (a) being atomic, i.e. not being…
With AI systems widely applied to assist humans in decision-making processes such as talent hiring, school admission, and loan approval; there is an increasing need to ensure that the decisions made are fair. One major challenge for…
The fair-ranking problem, which asks to rank a given set of items to maximize utility subject to group fairness constraints, has received attention in the fairness, information retrieval, and machine learning literature. Recent works,…
Real-life tools for decision-making in many critical domains are based on ranking results. With the increasing awareness of algorithmic fairness, recent works have presented measures for fairness in ranking. Many of those definitions…
The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…
Many computational problems can be modelled as the class of all finite structures $\mathbb A$ that satisfy a fixed first-order sentence $\phi$ hereditarily, i.e., we require that every (induced) substructure of $\mathbb A$ satisfies $\phi$.…
In fair division of indivisible goods, using sequences of sincere choices (or picking sequences) is a natural way to allocate the objects. The idea is as follows: at each stage, a designated agent picks one object among those that remain.…
AI alignment and participatory design motivate a new democratic design problem: how to collectively choose a decision rule to use repeatedly. We study this problem for linear ranking rules, which repeatedly rank items $x_j$ within batches…
A Condorcet winning set addresses the Condorcet paradox by selecting a few candidates--rather than a single winner--such that no unselected alternative is preferred to all of them by a majority of voters. This idea extends to…
Coalition formation is a key problem in automated negotiation among self-interested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can do things more…
The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on…
We investigate lifted inference on ordered domains with predecessor relations, where the elements of the domain respect a total (cyclic) order, and every element has a distinct (clockwise) predecessor. Previous work has explored this…
We investigate the problem of random assignment of indivisible goods, in which each agent has an ordinal preference and a constraint. Our goal is to characterize the conditions under which there always exists a random assignment that…
To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings,…
Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…