Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals

@article{Huang2018OnlineVB,
  title={Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals},
  author={Zhiyi Huang and Z. Tang and Xiaowei Wu and Yuhao Zhang},
  journal={ArXiv},
  year={2018},
  volume={abs/1804.07458}
}
We introduce a weighted version of the ranking algorithm by Karp et al. (STOC 1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order. Our result shows that random arrivals help beating the 1-1/e barrier even in the vertex-weighted case. We build on the randomized primal-dual framework by Devanur et al. (SODA 2013) and design a two dimensional gain sharing function, which depends not only on the rank of… Expand
Online Vertex-Weighted Bipartite Matching
TLDR
This work builds on the randomized primal-dual framework by Devanur et al. (SODA 2013) and design a two dimensional gain sharing function, which depends not only on the rank of the offline vertex, but also on the arrival time of the online vertex, and proves a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order. Expand
Edge-Weighted Online Bipartite Matching
TLDR
This paper presents the first online algorithm that breaks the long-standing 1/2 barrier and achieves a competitive ratio of at least 0.5086, and can be seen as strong evidence that edge-weighted bipartite matching is strictly easier than submodular welfare maximization in the online setting. Expand
Tight Competitive Ratios of Classic Matching Algorithms in the Fully Online Model
TLDR
This paper pins down two tight competitive ratios of classic algorithms for the fully online matching problem and shows a tight competitive ratio of 0.567 for the ranking algorithm on bipartite graphs, matching a hardness result by Huang et al. (STOC 2018). Expand
Online Weighted Matching with a Sample
TLDR
The greedy-based online algorithm for edge-weighted matching with (one-sided) vertex arrivals in bipartite graphs, and edge arrivals in general graphs is studied, and the state-of-the-art single-sample prophet inequality for this problem is improved upon. Expand
Online Matching with General Arrivals
TLDR
The basic question of whether randomization allows one to beat the trivially-optimal deterministic competitive ratio of 1/2 for either of these natural arrival models is resolved, and there exists a randomized online matching algorithm. Expand
Online stochastic matching, poisson arrivals, and the natural linear program
TLDR
This work proposes a natural linear program for the Poisson arrival model, and demonstrates how to exploit its structure by introducing a converse of Jensen's inequality, and designs an algorithmic amortization to replace the analytic one in previous work. Expand
Vertex-weighted Online Stochastic Matching with Patience Constraints
TLDR
The stochasticity gap is defined for evaluating the usefulness of an LP formulation and bound this gap for a commonly used LP and a new algorithm is presented, achieving the first constant competitive ratio for this and several related problems. Expand
Online Graph Matching Problems with a Worst-Case Reassignment Budget
TLDR
This paper proposes to consider the general question of how requiring a non-amortized hard budget $k$ on the number of reassignments affects the algorithms' performances, under various models from the literature. Expand
Online Weighted Bipartite Matching with a Sample
TLDR
This work studies the classical online bipartite matching problem and analyzes a natural algorithmic framework that decides how to match an arriving vertex v by applying an offline matching algorithm to v and the sample and proves that it is tight. Expand
D S ] 2 1 A ug 2 02 0 GREEDY APPROACHES TO ONLINE STOCHASTIC MATCHING
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 anExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 35 REFERENCES
Online vertex-weighted bipartite matching and single-bid budgeted allocations
TLDR
The main result is an optimal (1−1/e)-competitive randomized algorithm for general vertex weights that effectively solves the problem of online budgeted allocations in the case when an agent makes the same bid for any desired item, even if the bid is comparable to his budget. Expand
How to match when all vertices arrive online
TLDR
A fully online model of maximum cardinality matching in which all vertices arrive online, and a novel charging mechanic is brought into the randomized primal dual technique by Devanur et al. (SODA 2013), allowing a vertex other than the two endpoints of a matched edge to share the gain. Expand
Online Stochastic Weighted Matching: Improved Approximation Algorithms
TLDR
The first approximation (0.667-competitive) algorithm for the online stochastic weighted matching problem beating the 1−1 / e barrier is presented and the approximation factor is improved by computing a careful third pseudo-matching along with the two offline solutions, and using it in the online algorithm. Expand
Randomized Primal-Dual analysis of RANKING for Online BiPartite Matching
TLDR
This is the first instance of a non-trivial randomized primal-dual algorithm in which the dual constraints only hold in expectation. Expand
Online bipartite matching with random arrivals: an approach based on strongly factor-revealing LPs
TLDR
This paper studies the ranking algorithm in the random arrivals model, and shows that it has a competitive ratio of at least 0.696, beating the 1-1/e ≈ 0.632 barrier in the adversarial model. Expand
Online bipartite matching with unknown distributions
TLDR
This is the first analysis to show an algorithm which breaks the natural 1 - 1/e -barrier' in the unknown distribution model (the authors' analysis in fact works in the stricter, random order model) and answers an open question in [GM08]. Expand
Online Stochastic Matching: Beating 1-1/e
TLDR
A novel application of the idea of the power of two choices from load balancing, which compute two disjoint solutions to the expected instance, and use both of them in the online algorithm in a prescribed preference order to characterize an upper bound for the optimum in any scenario. Expand
Improved Bounds for Online Stochastic Matching
TLDR
It is shown that the best competitive ratio that can be obtained with the static analysis used in the d-SM algorithm is upper bounded by 0.76, thus suggesting that a dynamic analysis may be needed to improve the competitive ratio significantly. Expand
Ranking on Arbitrary Graphs: Rematch via Continuous LP with Monotone and Boundary Condition Constraints
TLDR
The Ranking algorithm is revisited using the LP framework, and new duality and complementary slackness characterizations are introduced that can handle the monotone and the boundary constraints in continuous LP. Expand
Randomized Online Matching in Regular Graphs
TLDR
This work presents a novel randomized algorithm with competitive ratio tending to one on this family of graphs, under adversarial arrival order, and shows the convergence rate of the algorithm's competitive ratio to one is nearly tight, as no algorithm achieves competitive ratio better than [EQUATION]. Expand
...
1
2
3
4
...