Abstract
Graph expansion analysis of computational DAGs is useful for obtaining communication cost lower bounds where previous methods, such as geometric embedding, are not applicable. This has recently been demonstrated for Strassen’s and Strassen-like fast square matrix multiplication algorithms. Here we extend the expansion analysis approach to fast algorithms for rectangular matrix multiplication, obtaining a new class of communication cost lower bounds. These apply, for example to the algorithms of Bini et al. (1979) and the algorithms of Hopcroft and Kerr (1971). Some of our bounds are proved to be optimal.
| Original language | American English |
|---|---|
| Title of host publication | Design and Analysis of Algorithms - 1st Mediterranean Conference on Algorithms, MedAlg 2012, Proceedings |
| Editors | Guy Even, Dror Rawitz |
| Publisher | Springer Science and Business Media Deutschland GmbH |
| Pages | 13-36 |
| Number of pages | 24 |
| ISBN (Print) | 9783642348617 |
| DOIs | |
| State | Published - 2012 |
| Externally published | Yes |
| Event | 1st Mediterranean Conference on Algorithms, MedAlg 2012 - Kibbutz Ein Gedi, Israel Duration: 3 Dec 2012 → 5 Dec 2012 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 7659 LNNS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Conference
| Conference | 1st Mediterranean Conference on Algorithms, MedAlg 2012 |
|---|---|
| Country/Territory | Israel |
| City | Kibbutz Ein Gedi |
| Period | 3/12/12 → 5/12/12 |
Bibliographical note
Funding Information:★ Research supported by Microsoft (Award #024263) and Intel (Award #024894) funding and by matching funding by U.C. Discovery (Award #DIG07-10227). Additional support comes from Par Lab affiliates National Instruments, Nokia, NVIDIA, Oracle, and Samsung. ★★ Research is also supported by DOE grants DE-SC0003959, DESC0004938, and DE-AC02-05CH11231. ★★★ Research supported by the Sofja Kovalevskaja programme of Alexander von Hum-boldt Foundation and by the National Science Foundation under agreement DMS-0635607. † Research supported by U.S. Department of Energy grants under Grant Numbers DE-SC0003959.
Funding Information:
Research supported by Microsoft (Award #024263) and Intel (Award #024894) funding and by matching funding by U.C. Discovery (Award #DIG07-10227). Additional support comes from Par Lab affiliates National Instruments, Nokia, NVIDIA, Oracle, and Samsung.?? Research is also supported by DOE grants DE-SC0003959, DE-SC0004938, and DE-AC02-05CH11231.??? Research supported by the Sofja Kovalevskaja programme of Alexander von Humboldt Foundation and by the National Science Foundation under agreement DMS0635607.? Research supported by U.S. Department of Energy grants under Grant Numbers DE-SC0003959.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2012.