Related papers: The popular assignment problem: when cardinality i…
The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation. We consider the problem with the additional feature that agents' preferences involve uncertainty. The setting with…
We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor. If $G$ is bipartite then one can…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
We consider the task of allocating indivisible items to agents, when the agents' preferences over the items are identical. The preferences are captured by means of a directed acyclic graph, with vertices representing items and an edge…
In bipartite matching problems, vertices on one side of a bipartite graph are paired with those on the other. In its online variant, one side of the graph is available offline, while the vertices on the other side arrive online. When a…
A bipartite graph $G=(L,R;E)$ with at least one edge is said to be identifiable if for every vertex $v\in L$, the subgraph induced by its non-neighbors has a matching of cardinality $|L|-1$. An $\ell$-subgraph of $G$ is an induced subgraph…
The exact matching problem is a constrained variant of the maximum matching problem: given a graph with each edge having a weight $0$ or $1$ and an integer $k$, the goal is to find a perfect matching of weight exactly $k$. Mulmuley,…
Bipartite ranking is a fundamental supervised learning problem, with the goal of learning a ranking over instances with maximal Area Under the ROC Curve (AUC) against a single binary target label. However, one may often observe multiple…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
Suppose we are given a bipartite graph that admits a perfect matching and an adversary may delete any edge from the graph with the intention of destroying all perfect matchings. We consider the task of adding a minimum cost edge-set to the…
The Assignment problem is a fundamental and well-studied problem in the intersection of Social Choice, Computational Economics and Discrete Allocation. In the Assignment problem, a group of agents expresses preferences over a set of items,…
We study the problem of fair and efficient allocation of a set of indivisible chores to agents with additive cost functions. We consider the popular fairness notion of envy-freeness up to one good (EF1) with the efficiency notion of…
The \textsc{Bipartite Contraction} problem is to decide, given a graph $G$ and a parameter $k$, whether we can can obtain a bipartite graph from $G$ by at most $k$ edge contractions. The fixed-parameter tractability of the problem was shown…
The $k$-cardinality assignment problem asks for finding a maximal (minimal) weight of a matching of cardinality $k$ in a weighted bipartite graph $K_{n,n}$, $k \leq n$. The algorithm of Gassner and Klinz from 2010 for the parametric…
We study ex-post fairness in the object allocation problem where objects are valuable and commonly owned. A matching is fair from individual perspective if it has only inevitable envy towards agents who received most preferred objects --…
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
A 2-packing set for an undirected graph $G=(V,E)$ is a subset $\mathcal{S} \subset V$ such that any two vertices $v_1,v_2 \in \mathcal{S}$ have no common neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem. We…
For a set A of n applicants and a set I of m items, we consider a problem of computing a matching of applicants to items, i.e., a function M mapping A to I; here we assume that each applicant $x \in A$ provides a preference list on items in…
We consider the problem of allocating applicants to courses, where each applicant has a subset of acceptable courses that she ranks in strict order of preference. Each applicant and course has a capacity, indicating the maximum number of…
Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N and W be the node count, the largest edge weight and the total weight of G. Let k(x,y) be log(x)/log(x^2/y). We present a new…