Improved bounds for randomized preemptive online matching

Epstein, Leah; Levin, Asaf; Segev, Danny; Weimann, Oren

doi:10.1016/j.ic.2017.12.002

Cited by 24 publications

(51 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that previous hardness results for online matching and its variants [7,26,41,43] were stated, or can be recast, as hardness results for fractional algorithms. This approach, standard in the online algorithms literature, relies on the simple observation that any randomized algorithm A naturally induces a fractional algorithm A with the same competitive ratio, by assigning each edge (i, t) a value equal to its expected value according to A.…”

Section: Hardness Resultsmentioning

confidence: 90%

Randomized Online Matching in Regular Graphs

Cohen

Wajc

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

In this paper we study the classic online matching problem, introduced in the seminal work of Karp, Vazirani and Vazirani (STOC 1990), in regular graphs. For such graphs, an optimal deterministic algorithm as well as efficient algorithms under stochastic input assumptions were known. In this work, we present a novel randomized algorithm with competitive ratio tending to one on this family of graphs, under adversarial arrival order. Our main contribution is a novel algorithm which achieves competitive ratio 1In contrast, we show that all previously-studied online algorithms have competitive ratio strictly bounded away from one. Moreover, we show the convergence rate of our algorithm's competitive ratio to one is nearly tight, as no algorithm achieves competitive ratio better than 1 − O 1/ √ d . Finally, we show that our algorithm yields a similar competitive ratio with high probability, as well as guaranteeing each vertex a probability of being matched tending to one.

show abstract

Section: Hardness Resultsmentioning

confidence: 90%

Randomized Online Matching in Regular Graphs

Cohen

Wajc

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

show abstract

“…On the hardness front, the problem is known to be strictly harder than the one-sided vertex arrival model of Karp et al [18], which admits a competitive ratio of 1 − 1 /e ≈ 0.632. In particular, Epstein et al [10] gave an upper bound of 1 1+ln 2 ≈ 0.591 for this problem, recently improved by Huang et al [16] to 2− √ 2 ≈ 0.585. (Both bounds apply even to online algorithms with preemption; i.e., allowing edges to be removed from the matching in favor of a newly-arrived edge.)…”

Section: Prior Work and Our Resultsmentioning

confidence: 94%

“…Edge Arrivals. All prior upper bounds in the online literature [3,10,11,16,18] can be rephrased as upper bounds for fractional algorithms; i.e., algorithms which immediately and irrevocably assign each edge e a value x e on arrival, so that x is contained in the fractional matching polytope,…”

Section: Our Techniquesmentioning

confidence: 99%

Online Matching with General Arrivals

Gamlath

Kapralov

Maggiori

et al. 2019

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)

View full text Add to dashboard Cite

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 deterministic and randomized algorithms for this setting. In comparison, more general arrival models, such as edge arrivals and general vertex arrivals, have proven more challenging and positive results are known only for various relaxations of the problem. In particular, even the basic question of whether randomization allows one to beat the trivially-optimal deterministic competitive ratio of 1 /2 for either of these models was open. In this paper, we resolve this question for both these natural arrival models, and show the following.1. For edge arrivals, randomization does not help -no randomized algorithm is better than

show abstract

“…We also construct a matching hard instance for Water-Filling. The hardness result applies to arbitrary algorithms if we consider edge arrival models [BST17], even when preemptions are allowed [ELSW13,McG05], improving the best known bounds in these models. The second result focuses on the integral problem and the Ranking algorithm.…”

Section: Introduction 1our Contributions and Techniquesmentioning

confidence: 87%

“…The hardness result in this paper improves the bounds for the following online matching models. In online preemptive matching [ELSW13,McG05], each edge arrives online and the algorithm must immediately decide whether to add the edge to the matching and to dispose of previously selected edges if needed. A harder edge-arrival model [BST17] forbids edge disposals.…”

Section: Other Related Workmentioning

confidence: 99%

Tight Competitive Ratios of Classic Matching Algorithms in the Fully Online Model

Huang

Peng

Tang

et al. 2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

Huang et al. (STOC 2018) introduced the fully online matching problem, a generalization of the classic online bipartite matching problem in that it allows all vertices to arrive online and considers general graphs. They showed that the ranking algorithm by Karp et al. (STOC 1990) is strictly better than 0.5-competitive and the problem is strictly harder than the online bipartite matching problem in that no algorithms can be (1 − 1/e)-competitive.This paper pins down two tight competitive ratios of classic algorithms for the fully online matching problem. For the fractional version of the problem, we show that a natural instantiation of the water-filling algorithm is 2 − √ 2 ≈ 0.585-competitive, together with a matching hardness result. Interestingly, our hardness result applies to arbitrary algorithms in the edgearrival models of the online matching problem, improving the state-of-art 1 1+ln 2 ≈ 0.5906 upper bound. For integral algorithms, we show a tight competitive ratio of ≈ 0.567 for the ranking algorithm on bipartite graphs, matching a hardness result by Huang et al. (STOC 2018).

show abstract

Improved bounds for randomized preemptive online matching

Cited by 24 publications

References 30 publications

Randomized Online Matching in Regular Graphs

Randomized Online Matching in Regular Graphs

Online Matching with General Arrivals

Tight Competitive Ratios of Classic Matching Algorithms in the Fully Online Model

Contact Info

Product

Resources

About