2018
DOI: 10.1007/s00453-018-0505-7
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Online Algorithms for Maximum Cardinality Matching with Edge Arrivals

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Cited by 18 publications
(32 citation statements)
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“…(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.) On the positive side, as pointed out by Buchbinder et al [3], the edge arrival model has proven challenging, and results beating the 1 /2 competitive ratio were only achieved under various relaxations, including: random order edge arrival [14], bounded number of arrival batches [20], on trees, either with or without preemption [3,24], and for bounded-degree graphs [3]. The above papers all asked whether there exists a randomized ( 1 /2 + Ω(1))-competitive algorithm for adversarial edge arrivals (see also Open Question 17 in Mehta's survey [22]).…”
Section: Prior Work and Our Resultsmentioning
confidence: 76%
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“…(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.) On the positive side, as pointed out by Buchbinder et al [3], the edge arrival model has proven challenging, and results beating the 1 /2 competitive ratio were only achieved under various relaxations, including: random order edge arrival [14], bounded number of arrival batches [20], on trees, either with or without preemption [3,24], and for bounded-degree graphs [3]. The above papers all asked whether there exists a randomized ( 1 /2 + Ω(1))-competitive algorithm for adversarial edge arrivals (see also Open Question 17 in Mehta's survey [22]).…”
Section: Prior Work and Our Resultsmentioning
confidence: 76%
“…The answer is "yes" for fractional algorithms, as shown by combining our Theorem 1.1 with the 0.526-competitive fractional online matching algorithm under general vertex arrivals of Wang and Wong [25]. For integral online matching, however, the problem has proven challenging, and the only positive results for this problem, too, are for various relaxations, such as restriction to trees, either with or without preemption [3,4,24], for bounded-degree graphs [3], or (recently) allowing vertices to be matched during some known time interval [15,16].…”
Section: Prior Work and Our Resultsmentioning
confidence: 98%
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