{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T07:21:43Z","timestamp":1777965703334,"version":"3.51.4"},"reference-count":35,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2018,8,28]],"date-time":"2018-08-28T00:00:00Z","timestamp":1535414400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"DARPA SIMPLEX"},{"name":"NSF CAREER","award":["CCF-1053605"],"award-info":[{"award-number":["CCF-1053605"]}]},{"name":"center of excelence CE-ITI","award":["P202\/12\/G061 of GA \u010cR"],"award-info":[{"award-number":["P202\/12\/G061 of GA \u010cR"]}]},{"name":"DARPA GRAPHS\/AFOSR","award":["FA9550-12-1-0423"],"award-info":[{"award-number":["FA9550-12-1-0423"]}]},{"name":"NSF BIGDATA","award":["IIS-1546108"],"award-info":[{"award-number":["IIS-1546108"]}]},{"name":"NSF AF:Medium","award":["CCF-1161365"],"award-info":[{"award-number":["CCF-1161365"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2018,10,31]]},"abstract":"<jats:p>\n            We consider the problem of estimating the size of a maximum matching when the edges are revealed in a streaming fashion. When the input graph is planar, we present a simple and elegant streaming algorithm that, with high probability, estimates the size of a maximum matching within a constant factor using \u00d5(\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>2\/3<\/jats:sup>\n            ) space, where\n            <jats:italic>n<\/jats:italic>\n            is the number of vertices. The approach generalizes to the family of graphs that have bounded arboricity, which include graphs with an excluded constant-size minor. To the best of our knowledge, this is the first result for estimating the size of a maximum matching in the\n            <jats:italic>adversarial-order<\/jats:italic>\n            streaming model (as opposed to the random-order streaming model) in\n            <jats:italic>o<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            ) space. We circumvent the barriers inherent in the adversarial-order model by exploiting several structural properties of planar graphs, and more generally, graphs with bounded arboricity. We further reduce the required memory size to \u00d5(\u221a\n            <jats:italic>n<\/jats:italic>\n            ) for three restricted settings: (i) when the input graph is a forest; (ii) when we have 2-passes and the input graph has bounded arboricity; and (iii) when the edges arrive in random order and the input graph has bounded arboricity.\n          <\/jats:p>\n          <jats:p>\n            Finally, we design a reduction from the Boolean Hidden Matching Problem to show that there is no randomized streaming algorithm that estimates the size of the maximum matching to within a factor better than 3\/2 and uses only\n            <jats:italic>o<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>1\/2<\/jats:sup>\n            ) bits of space. Using the same reduction, we show that there is no deterministic algorithm that computes this kind of estimate in\n            <jats:italic>o<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            ) bits of space. The lower bounds hold even for graphs that are collections of paths of constant length.\n          <\/jats:p>","DOI":"10.1145\/3230819","type":"journal-article","created":{"date-parts":[[2018,8,30]],"date-time":"2018-08-30T13:45:11Z","timestamp":1535636711000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Streaming Algorithms for Estimating the Matching Size in Planar Graphs and Beyond"],"prefix":"10.1145","volume":"14","member":"320","published-online":{"date-parts":[[2018,8,28]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","unstructured":"Kook Jin Ahn and Sudipto Guha. 2011. Linear programming in the semi-streaming model with application to the maximum matching problem. In ICALP (2). 526--538.","DOI":"10.5555\/2027223.2027277"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1007352.1007379"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2011.89"},{"key":"e_1_2_1_4_1","volume-title":"Graph Theory with Applications","author":"Bondy John Adrian","unstructured":"John Adrian Bondy and Uppaluri Siva Ramachandra Murty. 1976. Graph Theory with Applications. Vol. 6. Macmillan London."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-011-9556-8"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-011-9556-8"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/100801901"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.09.013"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/070683155"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/070706550"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","unstructured":"Ashish Goel Michael Kapralov and Sanjeev Khanna. 2012. On the communication and streaming complexity of maximum bipartite matching. In SODA. 468--485.","DOI":"10.5555\/2095116.2095157"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","unstructured":"Manoj Gupta and Richard Peng. 2013. Fully dynamic (1 + &epsi;)-approximate matchings. In FOCS. 548--557. 10.1109\/FOCS.2013.65","DOI":"10.1109\/FOCS.2013.65"},{"key":"e_1_2_1_13_1","volume-title":"Proceedings of the 28th Annual IEEE Conference on Computational Complexity (CCC)","author":"Guruswami V.","year":"2013","unstructured":"V. Guruswami and K. Onak. 2013. Superlinear lower bounds for multipass graph processing. Proceedings of the 28th Annual IEEE Conference on Computational Complexity (CCC) (2013), 287--298."},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-69311-6_19"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2009.77"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.5555\/647674.731515"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.5555\/2627817.2627938"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.5555\/2634074.2634129"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/100216.100262"},{"key":"e_1_2_1_20_1","doi-asserted-by":"crossref","unstructured":"Christian Konrad Fr\u00e9d\u00e9ric Magniez and Claire Mathieu. 2012. Maximum matching in semi-streaming with few passes. In APPROX-RANDOM. 231--242.","DOI":"10.1007\/978-3-642-32512-0_20"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579141"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","unstructured":"L. Lovasz and M.D. Plummer. 1986. Matching theory. In North-Holland Amsterdam-New York.","DOI":"10.5555\/1096488"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/11538462_15"},{"key":"e_1_2_1_24_1","volume-title":"Encyclopedia of Database Systems. 1271--1275.","author":"McGregor A.","unstructured":"A. McGregor. 2009. Graph mining on streams. In Encyclopedia of Database Systems. 1271--1275."},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1980.12"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/2488608.2488703"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2008.81"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","unstructured":"Krzysztof Onak Dana Ron Michal Rosen and Ronitt Rubinfeld. 2012. A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size. In SODA. 1123--1131.","DOI":"10.5555\/2095116.2095204"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/1806689.1806753"},{"key":"e_1_2_1_30_1","volume-title":"Retrieved","year":"2018","unstructured":"P60. List of Open Problems in Sublinear Algorithms: Problem 60. Retrieved August 13, 2018 from http:\/\/sublinear.info\/60."},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793250767"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.5555\/1280283.1280327"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.5555\/2133036.2133038"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/1536414.1536447"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-010-9438-5"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3230819","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3230819","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:57:30Z","timestamp":1750208250000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3230819"}},"subtitle":[],"editor":[{"given":"Hossein","family":"Esfandiari","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Mohammadtaghi","family":"Hajiaghayi","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Vahid","family":"Liaghat","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Morteza","family":"Monemizadeh","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Krzysztof","family":"Onak","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2018,8,28]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,10,31]]}},"alternative-id":["10.1145\/3230819"],"URL":"https:\/\/doi.org\/10.1145\/3230819","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,28]]},"assertion":[{"value":"2016-03-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-05-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-08-28","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}