OpenLink Software

About: Cohn and Umans proposed a framework for developing fast matrix multiplication algorithms based on the embedding computation in certain groups algebras [9]. In subsequent work with Kleinberg and Szegedy, they connected this to the search for combinatorial objects called strong uniquely solvable puzzles (strong USPs) [8]. We begin a systematic computer-aided search for these objects. We develop and implement algorithms based on reductions to [Formula: see text] and [Formula: see text] to verify that puzzles are strong USPs and to search for large strong USPs. We produce tight bounds on the maximum size of a strong USP for width [Formula: see text], and construct puzzles of small width that are larger than previous work. Although our work only deals with puzzles of small-constant width and does not produce a new, faster matrix multiplication algorithm, we provide evidence that there exist families of strong USPs that imply matrix multiplication algorithms that are more efficient than those currently known.

 Permalink

an Entity references as follows:

Faceted Search & Find service v1.13.91

Alternative Linked Data Documents: Sponger | ODE     Raw Data in: CXML | CSV | RDF ( N-Triples N3/Turtle JSON XML ) | OData ( Atom JSON ) | Microdata ( JSON HTML) | JSON-LD    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] This material is Open Knowledge Creative Commons License Valid XHTML + RDFa
This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.
OpenLink Virtuoso version 07.20.3229 as of Jul 10 2020, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (94 GB total memory)
Copyright © 2009-2025 OpenLink Software