相关论文: Set systems related to a house allocation problem

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 generalize the classical nuts and bolts problem to a setting where the input is a collection of $n$ nuts and $m$ bolts, and there is no promise of any matching pairs. It is not allowed to compare a nut directly with a nut or a bolt…

The Bollob\'as set pairs inequality is a fundamental result in extremal set theory with many applications. In this paper, for $n \geq k \geq t \geq 2$, we consider a collection of $k$ families $\mathcal{A}_i: 1 \leq i \leq k$ where…

When allocating indivisible objects via lottery, planners often use ordinal mechanisms, which elicit agents' rankings of objects rather than their full preferences over lotteries. In such an ordinal informational environment, planners…

With spectrum auctions as our prime motivation, in this paper we analyze combinatorial auctions where agents' valuations exhibit complementarities. Assuming that the agents only value bundles of size at most $k$ and also assuming that we…

We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…

Inspired by real-world applications such as the assignment of pupils to schools or the allocation of social housing, the one-sided matching problem studies how a set of agents can be assigned to a set of objects when the agents have…

The allocation of scarce donor organs constitutes one of the most consequential algorithmic challenges in healthcare. While the field is rapidly transitioning from rigid, rule-based systems to machine learning and data-driven optimization,…

A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…

The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…

We consider collective decision making when the society consists of groups endowed with voting weights. Each group chooses an internal rule that specifies the allocation of its weight to the alternatives as a function of its members'…

The problem of fairly allocating a set of indivisible items is a well-known challenge in the field of (computational) social choice. In this scenario, there is a fundamental incompatibility between notions of fairness (such as envy-freeness…

Preference handling and optimization are indispensable means for addressing non-trivial applications in Answer Set Programming (ASP). However, their implementation becomes difficult whenever they bring about a significant increase in…

The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…

We study maximum selection and sorting of $n$ numbers using pairwise comparators that output the larger of their two inputs if the inputs are more than a given threshold apart, and output an adversarially-chosen input otherwise. We consider…

A family $\mathcal F$ has covering number $\tau$ if the size of the smallest set intersecting all sets from $\mathcal F$ is equal to $\tau$. Let $M(n,k,\tau)$ stand for the size of the largest intersecting family $\mathcal F$ of $k$-element…

We study housing markets as introduced by Shapley and Scarf (1974). We investigate the computational complexity of various questions regarding the situation of an agent $a$ in a housing market $H$: we show that it is $\mathsf{NP}$-hard to…

Most modern ticketing systems rely on a first-come-first-serve or randomized allocation system to determine the allocation of tickets. Such systems has received considerable backlash in recent years due to its inequitable allotment and…

Let $\mathcal{A}_1,\ldots,\mathcal{A}_m$ be families of $k$-subsets of an $n$-set. Suppose that one cannot choose pairwise disjoint edges from $s+1$ distinct families. Subject to this condition we investigate the maximum of…

We consider the allocation of indivisible objects when agents have preferences over their own allocations, but share the ownership of the resources to be distributed. Examples might include seats in public schools, faculty offices, and time…