Related papers: A Stable Marriage Requires Communication
A population protocol can be viewed as a sequence of pairwise interactions of $n$ agents (nodes). During one interaction, two agents selected uniformly at random update their states by applying a specified deterministic transition function.…
An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…
We study stable matching problems where agents have multilayer preferences: There are $\ell$ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences,…
In the marriage problem, a variant of the bi-parted matching problem, each member has a `wish-list' expressing his/her preference for all possible partners; this list consists of random, positive real numbers drawn from a certain…
We give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures $\Phi$ and $\Psi$ on $\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a…
A stable cutset is a set of vertices $S$ of a connected graph, that is pairwise non-adjacent and when deleting $S$, the graph becomes disconnected. Determining the existence of a stable cutset in a graph is known to be NP-complete. In this…
We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). In particular, we seek stable matchings that are optimal with respect to profile, which is a vector that indicates the…
We use an elementary argument building on group actions to prove that the selection-free steady state genetic algorithm analyzed by Sutton and Witt (GECCO 2019) takes an expected number of $\Omega(2^n / \sqrt n)$ iterations to find any…
Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable…
This research paper addresses the stability of search algorithms in complex networks when dealing with incomplete information or uncertainty. We propose a theoretical model to investigate whether a global search algorithm with incomplete…
Balanced and swap-robust minimal trades, introduced in [1], are important for studying the balance and stability of server access request protocols under data popularity changes. Constructions of such trades have so far relied on paired…
We consider the problem of maintaining the Euclidean Delaunay triangulation $\DT$ of a set $P$ of $n$ moving points in the plane, along algebraic trajectories of constant description complexity. Since the best known upper bound on the…
We revisit the majority problem in the population protocol communication model, as first studied by Angluin et al. (Distributed Computing 2008). We consider a more general version of this problem known as plurality consensus, which has…
Frei et al. [6] showed that the problem to decide whether a graph is stable with respect to some graph parameter under adding or removing either edges or vertices is $\Theta_2^{\text{P}}$-complete. They studied the common graph parameters…
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union…
We show a new lower bound on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally…
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
We present a method to design parallel algorithms for constrained combinatorial optimization problems. Our method solves and generalizes many classical combinatorial optimization problems including the stable marriage problem, the shortest…
An LLM is stable if it reaches the same conclusion when asked the identical question multiple times. We find leading LLMs like gpt-4o, claude-3.5, and gemini-1.5 are unstable when providing answers to hard legal questions, even when made as…
When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may…