Related papers: Online Stochastic Matching with Edge Arrivals
The online matching problem was introduced by Karp, Vazirani and Vazirani nearly three decades ago. In that seminal work, they studied this problem in bipartite graphs with vertices arriving only on one side, and presented optimal…
Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 - 1/e) competitive ratio in the standard…
For two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ defined on the same ground set $E$, the online matroid intersection problem is to design an algorithm that constructs a large common independent set in an online fashion. The algorithm is…
We consider Online Minimum Bipartite Matching under the uniform metric. We show that Randomized Greedy achieves a competitive ratio equal to $(1+1/n) (H_{n+1}-1)$, which matches the lower bound. Comparing with the fact that RG achieves an…
We study the problem of online unweighted bipartite matching with $n$ offline vertices and $n$ online vertices where one wishes to be competitive against the optimal offline algorithm. While the classic RANKING algorithm of Karp et al.…
In this paper, we generalize the recently studied Stochastic Matching problem to more accurately model a significant medical process, kidney exchange, and several other applications. Up until now the Stochastic Matching problem that has…
Online bipartite matching and its variants are among the most fundamental problems in the online algorithms literature. Karp, Vazirani, and Vazirani (STOC 1990) introduced an elegant algorithm for the unweighted problem that achieves an…
Online bipartite matching has been extensively studied. In the unweighted setting, Karp et al. gave an optimal $(1 - 1/e)$-competitive randomized algorithm. In the weighted setting, optimal algorithms have been achieved only under…
Most practical scheduling applications involve some uncertainty about the arriving times and lengths of the jobs. Stochastic online scheduling is a well-established model capturing this. Here the arrivals occur online, while the processing…
Online bipartite matching with one-sided arrival and its variants have been extensively studied since the seminal work of Karp, Vazirani, and Vazirani (STOC 1990). Motivated by real-life applications with dynamic market structures, e.g.…
In the online bipartite matching with reassignments problem, an algorithm is initially given only one side of the vertex set of a bipartite graph; the vertices on the other side are revealed to the algorithm one by one, along with its…
We study online algorithms for maximum cardinality matchings with edge arrivals in graphs of low degree. Buchbinder, Segev, and Tkach showed that no online algorithm for maximum cardinality fractional matchings can achieve a competitive…
The online stochastic matching problem was introduced by [FMMM09], together with the $(1-\frac1e)$-competitive Suggested Matching algorithm. In the most general edge-weighted setting, this ratio has not been improved for more than one…
Online matching is a fundamental problem in the study of online algorithms. We study the problem under a very general arrival model: the edge arrival model. Free disposal is an important notion in the online matching literature, which…
We study the $b$-matching problem in bipartite graphs $G=(S,R,E)$. Each vertex $s\in S$ is a server with individual capacity $b_s$. The vertices $r\in R$ are requests that arrive online and must be assigned instantly to an eligible server.…
Inspired by sequential budgeted allocation problems, we study the online matching problem with budget refills. In this context, we consider an online bipartite graph $G=(U,V,E)$, where the nodes in $V$ are discovered sequentially and nodes…
We study generalizations of online bipartite matching in which each arriving vertex (customer) views a ranked list of offline vertices (products) and matches to (purchases) the first one they deem acceptable. The number of products that the…
Motivated by applications in online dating and kidney exchange, the stochastic matching problem was introduced by Chen, Immorlica, Karlin, Mahdian and Rudra (2009). They have proven a 4-approximation of a simple greedy strategy, but…
In the weighted bipartite matching problem, the goal is to find a maximum-weight matching in a bipartite graph with nonnegative edge weights. We consider its online version where the first vertex set is known beforehand, but vertices of the…
This article presents a simplification of Zadimoghaddam's algorithm for the edge-weighted online bipartite matching problem, under the online primal dual framework. In doing so, we obtain an improved competitive ratio of $0.514$. We first…