In a recent breakthrough, Paz and Schwartzman (SODA'17) presented a single-pass (2+epsilon)-approximation algorithm for the maximum weight matching problem in the semi-streaming model. Their algorithm uses O(n log^2 n) bits of space, for any constant epsilon>0. We present a simplified and more intuitive primal-dual analysis, for essentially the same algorithm, which also improves the space complexity to the optimal bound of O(n log n) bits - this is optimal as the output matching requires Omega(n log n) bits.
@InProceedings{ghaffari_et_al:OASIcs.SOSA.2019.13, author = {Ghaffari, Mohsen and Wajc, David}, title = {{Simplified and Space-Optimal Semi-Streaming (2+epsilon)-Approximate Matching}}, booktitle = {2nd Symposium on Simplicity in Algorithms (SOSA 2019)}, pages = {13:1--13:8}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-099-6}, ISSN = {2190-6807}, year = {2019}, volume = {69}, editor = {Fineman, Jeremy T. and Mitzenmacher, Michael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.13}, URN = {urn:nbn:de:0030-drops-100396}, doi = {10.4230/OASIcs.SOSA.2019.13}, annote = {Keywords: Streaming, Semi-Streaming, Space-Optimal, Matching} }
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