相关论文: The Complexity of Approximately Counting Stable Ro…

We examine the computational complexity of approximately counting the list H-colourings of a graph. We discover a natural graph-theoretic trichotomy based on the structure of the graph H. If H is an irreflexive bipartite graph or a…

We study the problem of assigning agents to the vertices of a graph such that no pair of neighbors can benefit from swapping assignments -- a property we term neighborhood stability. We further assume that agents' utilities are based solely…

$k$-means clustering is NP-hard in the worst case but previous work has shown efficient algorithms assuming the optimal $k$-means clusters are \emph{stable} under additive or multiplicative perturbation of data. This has two caveats. First,…

No feature ranking can be simultaneously faithful, stable, and complete when features are collinear. For collinear pairs, ranking reduces to a coin flip. We prove this impossibility, quantify it for four model classes, resolve it via…

A preference system $\mathcal{I}$ is an undirected graph where vertices have preferences over their neighbors, and $\mathcal{I}$ admits a master list if all preferences can be derived from a single ordering over all vertices. We study the…

We consider the problem of optimal recovery of true ranking of $n$ items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of $\Omega(n^2)$ for the…

Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…

We study the active learning problem of top-$k$ ranking from multi-wise comparisons under the popular multinomial logit model. Our goal is to identify the top-$k$ items with high probability by adaptively querying sets for comparisons and…

We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized…

We study the problem of learning to rank from pairwise preferences, and solve a long-standing open problem that has led to development of many heuristics but no provable results for our particular problem. Given a set $V$ of $n$ elements,…

We consider scheduling on identical and unrelated parallel machines with job assignment restrictions. These problems are NP-hard and they do not admit polynomial time approximation algorithms with approximation ratios smaller than $1.5$…

Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as…

While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this…

We study the Popular Matching problem in multiple models, where the preferences of the agents in the instance may change or may be unknown/uncertain. In particular, we study an Uncertainty model, where each agent has a possible set of…

We study the envy-free house allocation problem when agents have uncertain preferences over items and consider several well-studied preference uncertainty models. The central problem that we focus on is computing an allocation that has the…

We study the Student Project Allocation problem with lecturer preferences over Students (SPA-S), which involves the assignment of students to projects based on student preferences over projects, lecturer preferences over students, and…

We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…

We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…

It is shown in this note that approximating the number of independent sets in a $k$-uniform linear hypergraph with maximum degree at most $\Delta$ is NP-hard if $\Delta\geq 5\cdot 2^{k-1}+1$. This confirms that for the relevant sampling and…

In this paper we consider the classic scheduling problem of minimizing total weighted completion time on unrelated machines when jobs have release times, i.e, $R | r_{ij} | \sum_j w_j C_j$ using the three-field notation. For this problem, a…