TY - GEN
T1 - General Graphs are Easier than Bipartite Graphs
T2 - 23rd ACM Conference on Economics and Computation, EC 2022
AU - Ezra, Tomer
AU - Feldman, Michal
AU - Gravin, Nick
AU - Tang, Zhihao Gavin
N1 - Publisher Copyright:
© 2022 ACM.
PY - 2022/7/12
Y1 - 2022/7/12
N2 - Online algorithms for secretary matching in bipartite weighted graphs have been studied extensively in recent years. We generalize this study to secretary matching in general weighted graphs, for both vertex and edge arrival models. Under vertex arrival, vertices arrive online in a uniformly random order; upon the arrival of a vertex v, the weights of edges from v to all previously arriving vertices are revealed, and the algorithm decides which of these edges, if any, to include in the matching. We provide a tight 5/12-competitive algorithm for this setting. Interestingly, it outperforms the best possible algorithm for secretary matching in bipartite graphs with 1-sided arrival, which cannot be better than 1/e-competitive. Under edge arrival, edges arrive online in a uniformly random order; upon the arrival of an edge e, its weight is revealed, and the algorithm decides whether to include it in the matching or not. For this setting we provide a 1/4-competitive algorithm, which improves upon the state of the art bound.
AB - Online algorithms for secretary matching in bipartite weighted graphs have been studied extensively in recent years. We generalize this study to secretary matching in general weighted graphs, for both vertex and edge arrival models. Under vertex arrival, vertices arrive online in a uniformly random order; upon the arrival of a vertex v, the weights of edges from v to all previously arriving vertices are revealed, and the algorithm decides which of these edges, if any, to include in the matching. We provide a tight 5/12-competitive algorithm for this setting. Interestingly, it outperforms the best possible algorithm for secretary matching in bipartite graphs with 1-sided arrival, which cannot be better than 1/e-competitive. Under edge arrival, edges arrive online in a uniformly random order; upon the arrival of an edge e, its weight is revealed, and the algorithm decides whether to include it in the matching or not. For this setting we provide a 1/4-competitive algorithm, which improves upon the state of the art bound.
KW - online matching
KW - secretary problem
UR - http://www.scopus.com/inward/record.url?scp=85135042299&partnerID=8YFLogxK
U2 - 10.1145/3490486.3538290
DO - 10.1145/3490486.3538290
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AN - SCOPUS:85135042299
T3 - EC 2022 - Proceedings of the 23rd ACM Conference on Economics and Computation
SP - 1148
EP - 1177
BT - EC 2022 - Proceedings of the 23rd ACM Conference on Economics and Computation
PB - Association for Computing Machinery, Inc
Y2 - 11 July 2022 through 15 July 2022
ER -