相关论文: How to Match when All Vertices Arrive Online
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…
Online bipartite matching with edge arrivals remained a major open question for a long time until a recent negative result by [Gamlath et al. FOCS 2019], who showed that no online policy is better than the straightforward greedy algorithm,…
We study the performance of sequential contention resolution and matching algorithms on random graphs with vanishing edge probabilities. When the edges of the graph are processed in an adversarially-chosen order, we derive a new OCRS that…
Maximum cardinality matching in bipartite graphs is an important and well-studied problem. The fully dynamic version, in which edges are inserted and deleted over time has also been the subject of much attention. Existing algorithms for…
Within the context of stochastic probing with commitment, we consider the online stochastic matching problem; that is, the one sided online bipartite matching problem where edges adjacent to an online node must be probed to determine if…
We present an algorithm that finds a maximum cardinality $f$-matching of a simple graph in time $O(n^{2/3} m)$. Here $f:V\to \mathbb{N}$ is a given function, and an $f$-matching is a subgraph wherein each vertex $v\in V$ has degree $\le…
In the online hypergraph matching problem, hyperedges of size $k$ over a common ground set arrive online in adversarial order. The goal is to obtain a maximum matching (disjoint set of hyperedges). A na\"ive greedy algorithm for this…
The $b$-matching problem is an allocation problem where the vertices on the left-hand side of a bipartite graph, referred to as servers, may be matched multiple times. In the setting with stochastic rewards, an assignment between an…
Matching problems with group-fairness constraints and diversity constraints have numerous applications such as in allocation problems, committee selection, school choice, etc. Moreover, online matching problems have lots of applications in…
In the classic online graph balancing problem, edges arrive sequentially and must be oriented immediately upon arrival, to minimize the maximum in-degree. For adversarial arrivals, the natural greedy algorithm is $O(\log n)$-competitive,…
Online bipartite matching is a classical problem in online algorithms and we know that both the deterministic fractional and randomized integral online matchings achieve the same competitive ratio of $1-\frac{1}{e}$. In this work, we study…
This paper studies the maximum cardinality matching problem in stochastically evolving graphs. We formally define the arrival-departure model with stochastic departures. There, a graph is sampled from a specific probability distribution and…
We study the classical, randomized Ranking algorithm which is known to be $(1 - \frac{1}{e})$-competitive in expectation for the Online Bipartite Matching Problem. We give a tail inequality bound, namely that Ranking is $(1 - \frac{1}{e} -…
We investigate deterministic non-preemptive online scheduling with delayed commitment for total completion time minimization on parallel identical machines. In this problem, jobs arrive one-by-one and their processing times are revealed…
We study the classic online bipartite matching problem with a twist: offline vertices, called resources, are $\textit{reusable}$. In particular, when a resource is matched to an online vertex it is unavailable for a deterministic time…
Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…
This work presents an optimally-competitive algorithm for the problem of maximum weighted online perfect bipartite matching with i.i.d. arrivals. In this problem, we are given a known set of workers, a distribution over job types, and…
We study the minimum-cost metric perfect matching problem under online i.i.d arrivals. We are given a fixed metric with a server at each of the points, and then requests arrive online, each drawn independently from a known probability…
Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…
We study the online clustering problem where data items arrive in an online fashion. The algorithm maintains a clustering of data items into similarity classes. Upon arrival of v, the relation between v and previously arrived items is…