相关论文: Phase transition in the bipartite z-matching

We study the classical weighted perfect matchings problem for bipartite graphs or sometimes referred to as the assignment problem, i.e., given a weighted bipartite graph $G = (U\cup V,E)$ with weights $w : E \rightarrow \mathcal{R}$ we are…

In this paper we study the classic problem of computing a maximum cardinality matching in general graphs $G = (V, E)$. The best known algorithm for this problem till date runs in $O(m \sqrt{n})$ time due to Micali and Vazirani \cite{MV80}.…

In this paper we consider the well-studied problem of finding a perfect matching in a d-regular bipartite graph on 2n nodes with m=nd edges. The best-known algorithm for general bipartite graphs (due to Hopcroft and Karp) takes time…

We consider the problem of computing a matching in a bipartite graph in the presence of one-sided preferences. There are several well studied notions of optimality which include pareto optimality, rank maximality, fairness and popularity.…

Consider a matching problem on a graph where disjoint sets of vertices are privately owned by self-interested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to…

We present a weighted approach to compute a maximum cardinality matching in an arbitrary bipartite graph. Our main result is a new algorithm that takes as input a weighted bipartite graph $G(A\cup B,E)$ with edge weights of $0$ or $1$. Let…

In this paper, we consider the problem of computing an optimal matching in a bipartite graph where elements of one side of the bipartition specify preferences over the other side, and one or both sides can have capacities and…

A matching in a two-sided market often incurs an externality: a matched resource may become unavailable to the other side of the market, at least for a while. This is especially an issue in online platforms involving human experts as the…

An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…

Temporal graphs are introduced to model systems where the relationships among the entities of the system evolve over time. In this paper, we consider the temporal graphs where the edge set changes with time and all the changes are known a…

This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task…

In preference modelling, it is essential to determine the number of questions and their arrangements to ask from the decision maker. We focus on incomplete pairwise comparison matrices, and provide the optimal filling in patterns, which…

We study the maximum matching problem in the random-order semi-streaming setting. In this problem, the edges of an arbitrary $n$-vertex graph $G=(V, E)$ arrive in a stream one by one and in a random order. The goal is to have a single pass…

Bipartite networks manifest as a stream of edges that represent transactions, e.g., purchases by retail customers. Many machine learning applications employ neighborhood-based measures to characterize the similarity among the nodes, such as…

Bipartite b-matching is fundamental in algorithm design, and has been widely applied into economic markets, labor markets, etc. These practical problems usually exhibit two distinct features: large-scale and dynamic, which requires the…

We initiate the study of the Maximal Matching problem in bounded-deletion graph streams. In this setting, a graph $G$ is revealed as an arbitrary sequence of edge insertions and deletions, where the number of insertions is unrestricted but…

We study the oblivious matching problem, which aims at finding a maximum matching on a graph with unknown edge set. Any algorithm for the problem specifies an ordering of the vertex pairs. The matching is then produced by probing the pairs…

We perform an experimental study of algorithms for online bipartite matching under the known i.i.d. input model with integral types. In the last decade, there has been substantial effort in designing complex algorithms with the goal of…

The bipartite matching problem in the online and streaming settings has received a lot of attention recently. The classical vertex arrival setting, for which the celebrated Karp, Vazirani and Vazirani (KVV) algorithm achieves a $1-1/e$…

Applications in cloud platforms motivate the study of efficient load balancing under job-server constraints and server heterogeneity. In this paper, we study load balancing on a bipartite graph where left nodes correspond to job types and…