{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:29:29Z","timestamp":1750307369961,"version":"3.41.0"},"reference-count":26,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2010,5,1]],"date-time":"2010-05-01T00:00:00Z","timestamp":1272672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["6.07E+18","CCR-0093273"],"award-info":[{"award-number":["6.07E+18","CCR-0093273"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Des. Autom. Electron. Syst."],"published-print":{"date-parts":[[2010,5]]},"abstract":"<jats:p>Off-chip substrate routing for high-density packages is challenging due to requirements such as high density, lack of vertical detour, non-Manhattan routing, and primarily planar routing. The existing substrate routing algorithms often result in a large number of unrouted nets that have to be routed manually. This article develops an effective yet efficient diffusion-driven method D-Router to reduce congestion. Starting with an initial routing, we develop an effective diffusion-based congestion reduction. We iteratively find a congested window and spread out connections to reduce congestion inside the window by a simulated diffusion process based on the duality between congestion and concentration. The window is released after the congestion is eliminated. Compared with the state-of-the-art substrate routing method that leads to 480 nets unrouted for ten industrial designs with a total of 6415 nets, the D-Router reduces the amount of unrouted nets to 104, a reduction to the 4.6 multiple. In addition, the D-Router obtains a similar reduction on unrouted nets but runs up to 94 times faster when compared with a negotiation-based substrate routing.<\/jats:p>","DOI":"10.1145\/1754405.1754412","type":"journal-article","created":{"date-parts":[[2010,6,8]],"date-time":"2010-06-08T12:37:24Z","timestamp":1276000644000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Effective congestion reduction for IC package substrate routing"],"prefix":"10.1145","volume":"15","author":[{"given":"Shenghua","family":"Liu","sequence":"first","affiliation":[{"name":"Tsinghua University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoqiang","family":"Chen","sequence":"additional","affiliation":[{"name":"Magma Design Automation, Inc., San Jose, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tom Tong","family":"Jing","sequence":"additional","affiliation":[{"name":"University of California at Los Angeles, Los Angeles, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"He","sequence":"additional","affiliation":[{"name":"University of California at Los Angeles, Los Angeles, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robi","family":"Dutta","sequence":"additional","affiliation":[{"name":"Magma Design Automation, Inc., San Jose, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xian-Long","family":"Hong","sequence":"additional","affiliation":[{"name":"Tsinghua University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2010,6,10]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Bossen F. 1996. 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