{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T16:16:30Z","timestamp":1782317790596,"version":"3.54.5"},"reference-count":50,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1712119"],"award-info":[{"award-number":["CCF-1712119"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1740858"],"award-info":[{"award-number":["CCF-1740858"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1839274"],"award-info":[{"award-number":["DMS-1839274"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Visual. Comput. Graphics"],"published-print":{"date-parts":[[2022]]},"DOI":"10.1109\/tvcg.2022.3155564","type":"journal-article","created":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T20:37:19Z","timestamp":1646167039000},"page":"1-1","source":"Crossref","is-referenced-by-count":16,"title":["Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, (SGD)^2"],"prefix":"10.1109","author":[{"given":"Reyan","family":"Ahmed","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felice","family":"De Luca","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sabin","family":"Devkota","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stephen G","family":"Kobourov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mingwei","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-63938-1_67"},{"key":"ref38","first-page":"8024","article-title":"Pytorch: An imperative style, high-performance deep learning library","author":"paszke","year":"2019","journal-title":"Proc Int Conf Neural Inf Process"},{"key":"ref33","article-title":"Adam: A method for stochastic optimization","author":"kingma","year":"2014"},{"key":"ref32","article-title":"On large-batch training for deep learning: Generalization gap and sharp minima","author":"keskar","year":"2016"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(89)90102-6"},{"key":"ref30","first-page":"448","article-title":"Batch normalization: Accelerating deep network training by reducing internal covariate shift","author":"ioffe","year":"2015","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.3390\/app10196653"},{"key":"ref36","article-title":"Visualizing the loss landscape of neural nets","author":"li","year":"2017"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/BF02289565"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13187"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jvlc.2011.12.002"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"11","DOI":"10.25080\/TCWV9851","article-title":"Exploring network structure, dynamics, and function using networkx","author":"hagberg","year":"2008","journal-title":"Proc 7th Python Sci Conf"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/MCSE.2007.55"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-68766-3_1"},{"key":"ref1","first-page":"5","article-title":"The rectilinear crossing number of $k_{n}$kn: Closing in (or are we?)","author":"\u00e1brego","year":"0","journal-title":"Proc 30th Essays Geometric Graph Theory"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-27261-0_41"},{"key":"ref22","first-page":"483","article-title":"Graphviz–open source graph drawing tools","author":"ellson","year":"2001","journal-title":"Proc 9th Int Symp Graph Drawing"},{"key":"ref21","article-title":"A force-directed method for large crossing angle graph drawing","author":"eades","year":"2010"},{"key":"ref24","first-page":"239","article-title":"Graph drawing by stress majorization","author":"gansner","year":"2004","journal-title":"Proc Int Symp Graph Drawing"},{"key":"ref23","first-page":"388","article-title":"Planar preprocessing for spring embedders","author":"fowler","year":"2012","journal-title":"Proc Int Symp Graph Drawing"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717761"},{"key":"ref25","first-page":"5200","article-title":"SGD: General analysis and improved rates","author":"gower","year":"2019","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2018.2859997"},{"key":"ref10","article-title":"Keras","author":"chollet","year":"2015"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1145\/234535.234538"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975055.12"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1145\/2049662.2049663"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-04414-5_20"},{"key":"ref14","first-page":"575","article-title":"Graph drawing contest report","author":"devanny","year":"2017","journal-title":"Proc 25th Int Symp Graph Drawing Netw Vis"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-35802-0_23"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-37623-2_9"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01449.x"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.12.103"},{"key":"ref19","first-page":"393","article-title":"Layout with circular and other non-linear constraints using procrustes projection","author":"dwyer","year":"2009","journal-title":"Proc Int Symp Graph Drawing"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-04414-5_19"},{"key":"ref3","article-title":"On exponential convergence of SGD in non-convex over-parametrized learning","author":"bassily","year":"2018"},{"key":"ref6","first-page":"4413","article-title":"The lovász-softmax loss: A tractable surrogate for the optimization of the intersection-over-union measure in neural networks","author":"berman","year":"2018","journal-title":"Proc IEEE Conf Comput Vis Pattern Recognit"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1979.1675432"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2011.185"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2020.2990567"},{"key":"ref49","article-title":"ADADELTA: An adaptive learning rate method","author":"zeiler","year":"2012"},{"key":"ref9","first-page":"43","article-title":"Crossings and planarization","author":"buchheim","year":"2013","journal-title":"Handbook of Graph Drawing and Visualization"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2017.2745919"},{"key":"ref45","article-title":"Graph neural networks for graph drawing","author":"tiezzi","year":"2021"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1057\/palgrave.ivs.9500013"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2018.2864911"},{"key":"ref42","first-page":"1","article-title":"Optimal embedding of heterogeneous graph data with edge crossing constraints","author":"shabbeer","year":"0","journal-title":"Proc Int Conf Neural Inf Process Syst Workshop Challenges Data Vis"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.7155\/jgaa.00216"},{"key":"ref44","article-title":"Lecture 6.5—RmsProp: Divide the gradient by a running average of its recent magnitude","author":"tieleman","year":"2012"},{"key":"ref43","first-page":"309","article-title":"Tensorflow.js: Machine learning for the web and beyond","author":"smilkov","year":"2019","journal-title":"Proc Mach Learn Syst"}],"container-title":["IEEE Transactions on Visualization and Computer Graphics"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/2945\/4359476\/09723546.pdf?arnumber=9723546","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T16:05:05Z","timestamp":1726761905000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9723546\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"references-count":50,"URL":"https:\/\/doi.org\/10.1109\/tvcg.2022.3155564","relation":{},"ISSN":["1077-2626","1941-0506","2160-9306"],"issn-type":[{"value":"1077-2626","type":"print"},{"value":"1941-0506","type":"electronic"},{"value":"2160-9306","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]}}}