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Motivated by the serious problem that hospitals in rural areas suffer from a shortage of residents, we study the Hospitals/Residents model in which hospitals are associated with lower quotas and the objective is to satisfy them as much as…
In many-to-many matching models, substitutable preferences constitute the largest domain for which a pairwise stable matching is guaranteed to exist. In this note, we extend the recently proposed algorithm of Hatfield et al. [3] to test…
In real-world settings of the Deferred Acceptance stable matching algorithm, such as the American medical residency match (NRMP), school choice programs, and various national university entrance systems, candidates need to decide which…
In a stable matching problem there are two groups of agents, with agents on one side having their individual preferences for agents on another side as a potential match. It is assumed silently that agents can freely and costlessly ``switch"…
A line of work initiated by Fortnow in 1997 has proven model-independent time-space lower bounds for the $\mathsf{SAT}$ problem and related problems within the polynomial-time hierarchy. For example, for the $\mathsf{SAT}$ problem, the…
In iterative supervised learning algorithms it is common to reach a point in the search where no further induction seems to be possible with the available data. If the search is continued beyond this point, the risk of overfitting increases…
We reconsider a recently published algorithm (Dalkilic et al.) for merging lists by way of the perfect shuffle. The original publication gave only experimental results which, although consistent with linear execution time on the samples…
We study bandit learning in matching markets with two-sided reward uncertainty, extending prior research primarily focused on single-sided uncertainty. Leveraging the concept of `super-stability' from Irving (1994), we demonstrate the…
Dominating Set is a well-known combinatorial optimization problem which finds application in computational biology or mobile communication. Because of its $\mathrm{NP}$-hardness, one often turns to heuristics for good solutions. Many such…
Several works have shown unconditional hardness (via integrality gaps) of computing equilibria using strong hierarchies of convex relaxations. Such results however only apply to the problem of computing equilibria that optimize a certain…
We show that given a SM instance G as input we can find a largest collection of pairwise edge-disjoint stable matchings of G in time linear in the input size. This extends two classical results: 1. The Gale-Shapley algorithm, which can find…
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…
Focusing on the bipartite Stable Marriage problem, we investigate different robustness measures related to stable matchings. We analyze the computational complexity of computing them and analyze their behavior in extensive experiments on…
In this paper, we demonstrate that in many NP-complete variants of the stable matching problem, such as the Stable Hypergraph Matching problem, the Stable Multicommodity Flow problem, and the College Admission problem with common quotas, a…
We consider the online traveling salesman problem on the real line (OLTSPL) in which a salesman begins at the origin, traveling at no faster than unit speed along the real line, and wants to serve a sequence of requests, arriving online…
Many allocation problems in multiagent systems rely on agents specifying cardinal preferences. However, allocation mechanisms can be sensitive to small perturbations in cardinal preferences, thus causing agents who make ``small" or…
In function inversion, we are given a function $f: [N] \mapsto [N]$, and want to prepare some advice of size $S$, such that we can efficiently invert any image in time $T$. This is a well studied problem with profound connections to…
We provide improved space-time tradeoffs for permutation problems over additively idempotent semi-rings. In particular, there is an algorithm for the Traveling Salesperson Problem that solves $N$-vertex instances using space $S$ and time…
Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content…
In this paper, we focus on the problem of existence and computing of small and large stable models. We show that for every fixed integer k, there is a linear-time algorithm to decide the problem LSM (large stable models problem): does a…