Finding symmetries is a way to highlight shortcuts to answers that, for example, verify the safety of train schedules, identify bugs in software and hardware designs, or speed up common search tasks.
The algorithm is an update to software called "saucy" that the researchers developed in 2004 and shared with colleagues. Paul Darga, a graduate student in the Department of Electrical Engineering and Computer Science, will present the algorithm on June 10 at the Design Automation Conference in Anaheim, Calif. Darga's co-authors are Igor Markov, associate professor in the Department of Electrical Engineering and Computer Science, and Karem Sakallah, a professor in the same department.
The software's applications extend to artificial intelligence and logistics.It speeds up solutions to fundamental computer science problems and quickly solves what's called the graph automorphism problem. "Our new algorithm solves the graph automorphism problem so quickly in real-life applications that the problem is starting to look easy," Markov said.
Symmetries are, in a sense, interchangeable options that lead to the same outcome. In complicated equations, symmetries point to repeated branches of the search for solutions that only need to be figured out once. Current programs that look for symmetries can take days to give results even when they find no instances, Darga said. The new method finishes in seconds even when there are millions of variables.
To illustrate how finding symmetries can simplify equations, Markov pointed to the pigeonhole principle. This says you can't, for example, fit 10 birds in nine pigeonholes (unless they share.) The particular problem has a nine-fold symmetry because it doesn't matter which hole each bird occupies. One will always end up homeless. It also has a 10-fold symmetry because the birds are considered interchangeable.
"If you ask a computer to put 20 trains on 19 tracks, this computation may take forever," Markov said. "But if you use an approach with symmetry breaking, these cases can be solved in seconds."
Symmetry breaking in train scheduling and logistics can also help figure the shortest itineraries. In artificial intelligence, the ability to recognize symmetries quickly could help a computer generate a plan or an optimal schedule. The computer would know when the order of tasks was interchangeable.
The new algorithm starts working in the same way as existing symmetry breaking software. It converts the complicated equation into a graph and looks for similarities in the arrangement of the vertices. Like the original version of saucy, it narrows the search while exploiting what Darga calls "sparsity"---the fact that almost every node on the graph is only connected to a few other nodes.
The saucy update recognizes that it's not just the node connections that are sparse. It turns out that most important symmetries themselves are sparse too, in that they involve only several nodes at a time. Other symmetries can be derived from sparse symmetries, and the number of distinct symmetries can grow exponentially with the size of the system.
"Just like snowflakes, many interconnected systems in technology and nature are sparse and exhibit structural symmetries," Sakallah said. "The internet connectivity graph we worked with reminds me of a giant snowflake. It has a quarter million vertices and half a million edges, but it exhibits more symmetries than there are electrons in the universe."
In less than a half-second, the new software captured 1083,687 different symmetries in an Internet connectivity graph of routers around the world. A symmetry in this graph signifies a way the routers could be shuffled that wouldn't change the operation.
Previous methods timed out in the 30 minutes they were given to generate results in these experiments. Darga said it would take these older programs days to solve such a complicated problem. In searching for symmetries in the road networks between cities and towns in Illinois, the new algorithm captured the 104,843 symmetries in less than a half-second, whereas the most robust previous algorithm took 16 minutes.
The paper is called "Faster Symmetry Discovery Using Sparsity of Symmetries." It is available at http://www.eecs.umich.edu/~imarkov/pubs/conf/dac08-sym.pdf. Information about how to obtain the software is at http://vlsicad.eecs.umich.edu/BK/SAUCY/.For more information:
Nicole Casal Moore | alfa
New technology enables 5-D imaging in live animals, humans
16.01.2017 | University of Southern California
Fraunhofer FIT announces CloudTeams collaborative software development platform – join it for free
10.01.2017 | Fraunhofer-Institut für Angewandte Informationstechnik FIT
Researchers from the University of Hamburg in Germany, in collaboration with colleagues from the University of Aarhus in Denmark, have synthesized a new superconducting material by growing a few layers of an antiferromagnetic transition-metal chalcogenide on a bismuth-based topological insulator, both being non-superconducting materials.
While superconductivity and magnetism are generally believed to be mutually exclusive, surprisingly, in this new material, superconducting correlations...
Laser-driving of semimetals allows creating novel quasiparticle states within condensed matter systems and switching between different states on ultrafast time scales
Studying properties of fundamental particles in condensed matter systems is a promising approach to quantum field theory. Quasiparticles offer the opportunity...
Among the general public, solar thermal energy is currently associated with dark blue, rectangular collectors on building roofs. Technologies are needed for aesthetically high quality architecture which offer the architect more room for manoeuvre when it comes to low- and plus-energy buildings. With the “ArKol” project, researchers at Fraunhofer ISE together with partners are currently developing two façade collectors for solar thermal energy generation, which permit a high degree of design flexibility: a strip collector for opaque façade sections and a solar thermal blind for transparent sections. The current state of the two developments will be presented at the BAU 2017 trade fair.
As part of the “ArKol – development of architecturally highly integrated façade collectors with heat pipes” project, Fraunhofer ISE together with its partners...
At TU Wien, an alternative for resource intensive formwork for the construction of concrete domes was developed. It is now used in a test dome for the Austrian Federal Railways Infrastructure (ÖBB Infrastruktur).
Concrete shells are efficient structures, but not very resource efficient. The formwork for the construction of concrete domes alone requires a high amount of...
Many pathogens use certain sugar compounds from their host to help conceal themselves against the immune system. Scientists at the University of Bonn have now, in cooperation with researchers at the University of York in the United Kingdom, analyzed the dynamics of a bacterial molecule that is involved in this process. They demonstrate that the protein grabs onto the sugar molecule with a Pac Man-like chewing motion and holds it until it can be used. Their results could help design therapeutics that could make the protein poorer at grabbing and holding and hence compromise the pathogen in the host. The study has now been published in “Biophysical Journal”.
The cells of the mouth, nose and intestinal mucosa produce large quantities of a chemical called sialic acid. Many bacteria possess a special transport system...
10.01.2017 | Event News
09.01.2017 | Event News
05.01.2017 | Event News
17.01.2017 | Earth Sciences
17.01.2017 | Materials Sciences
17.01.2017 | Architecture and Construction