2020
DOI: 10.1007/s10878-020-00641-w
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Online maximum matching with recourse

Abstract: We study the online maximum matching problem in a model in which the edges are associated with a known recourse parameter k. An online algorithm for this problem has to maintain a valid matching while edges of the underlying graph are presented one after the other. At any moment the algorithm can decide to include an edge into the matching or to exclude it, under the restriction that at most k such actions per edge take place, where k is typically a small constant. This problem was introduced and studied in th… Show more

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Cited by 7 publications
(14 citation statements)
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“…There is a line of research on online matching problems with recourse. Angelopoulos et al [2] studied a more general setting for Maximum Cardinality Matching and showed that given that no element incurs more than k recourse, there exists an algorithm that attains a competitive ratio of 1 + O(1/ √ k). Megow and Nölke [20] showed that for the Min-Cost Bipartite Matching problem, constant competitiveness is achievable with amortized recourse O(log n), where n is the number of requests.…”
Section: Related Workmentioning
confidence: 99%
“…There is a line of research on online matching problems with recourse. Angelopoulos et al [2] studied a more general setting for Maximum Cardinality Matching and showed that given that no element incurs more than k recourse, there exists an algorithm that attains a competitive ratio of 1 + O(1/ √ k). Megow and Nölke [20] showed that for the Min-Cost Bipartite Matching problem, constant competitiveness is achievable with amortized recourse O(log n), where n is the number of requests.…”
Section: Related Workmentioning
confidence: 99%
“…Whereas late rejection has had significant focus, late acceptance was studied in [Boyar et al 2016], followed by a systematic study of all combinations of a number of classic graph problems combined with either late accept, late reject, or both (where late reject is irrevocable) in [Boyar et al 2017a], detailing the performance implications of each choice. In [Angelopoulos et al 2018], the work of [Boyar et al 2017a] was continued for the matching problem, considering more levels of late accept/reject.…”
Section: To Appear In Acm Computing Surveysmentioning
confidence: 99%
“…When an object (vertex or edge) arrives, we find a shortest (if the model is unweighted) or most profitable (if weighted) one among all augmenting paths that contain the object. 2 If such a path does not exist or is longer than k − 1, do nothing; otherwise, augment the matching along the path.…”
Section: Our Models and Algorithmmentioning
confidence: 99%
“…Although their model significantly differs from our proposed model, we note that their analysis, with hindsight, would have been useful in proving some special cases (k = 4) of Theorems 1 and 5. Angelopoulos, Dürr, and Jin [2] considered the case where the decision can be revoked at most k−1 times and gave a 1…”
mentioning
confidence: 99%