Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


'Saucy' Software Update Finds Symmetries Dramatically Faster

Computer scientists at the University of Michigan developed open-source software that cuts the time to find symmetries in complicated equations from days to seconds in some cases.

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 Information about how to obtain the software is at

For more information:
Paul Darga:
Igor Markov:
Karem Sakallah:
Design Automation Conference:
Michigan Engineering:
The University of Michigan College of Engineering is ranked among the top engineering schools in the country. At more than $130 million annually, its engineering research budget is one of largest of any public university. Michigan Engineering is home to 11 academic departments and a National Science Foundation Engineering Research Center. The college plays a leading role in the Michigan Memorial Phoenix Energy Institute and hosts the world class Lurie Nanofabrication Facility. Michigan Engineering's premier scholarship, multidisciplinary scope and international scale combine to create The Michigan Difference.

Nicole Casal Moore | alfa
Further information:

All articles from Information Technology >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: New 3-D wiring technique brings scalable quantum computers closer to reality

Researchers from the Institute for Quantum Computing (IQC) at the University of Waterloo led the development of a new extensible wiring technique capable of controlling superconducting quantum bits, representing a significant step towards to the realization of a scalable quantum computer.

"The quantum socket is a wiring method that uses three-dimensional wires based on spring-loaded pins to address individual qubits," said Jeremy Béjanin, a PhD...

Im Focus: Scientists develop a semiconductor nanocomposite material that moves in response to light

In a paper in Scientific Reports, a research team at Worcester Polytechnic Institute describes a novel light-activated phenomenon that could become the basis for applications as diverse as microscopic robotic grippers and more efficient solar cells.

A research team at Worcester Polytechnic Institute (WPI) has developed a revolutionary, light-activated semiconductor nanocomposite material that can be used...

Im Focus: Diamonds aren't forever: Sandia, Harvard team create first quantum computer bridge

By forcefully embedding two silicon atoms in a diamond matrix, Sandia researchers have demonstrated for the first time on a single chip all the components needed to create a quantum bridge to link quantum computers together.

"People have already built small quantum computers," says Sandia researcher Ryan Camacho. "Maybe the first useful one won't be a single giant quantum computer...

Im Focus: New Products - Highlights of COMPAMED 2016

COMPAMED has become the leading international marketplace for suppliers of medical manufacturing. The trade fair, which takes place every November and is co-located to MEDICA in Dusseldorf, has been steadily growing over the past years and shows that medical technology remains a rapidly growing market.

In 2016, the joint pavilion by the IVAM Microtechnology Network, the Product Market “High-tech for Medical Devices”, will be located in Hall 8a again and will...

Im Focus: Ultra-thin ferroelectric material for next-generation electronics

'Ferroelectric' materials can switch between different states of electrical polarization in response to an external electric field. This flexibility means they show promise for many applications, for example in electronic devices and computer memory. Current ferroelectric materials are highly valued for their thermal and chemical stability and rapid electro-mechanical responses, but creating a material that is scalable down to the tiny sizes needed for technologies like silicon-based semiconductors (Si-based CMOS) has proven challenging.

Now, Hiroshi Funakubo and co-workers at the Tokyo Institute of Technology, in collaboration with researchers across Japan, have conducted experiments to...

All Focus news of the innovation-report >>>



Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

Agricultural Trade Developments and Potentials in Central Asia and the South Caucasus

14.10.2016 | Event News

World Health Summit – Day Three: A Call to Action

12.10.2016 | Event News

Latest News

Resolving the mystery of preeclampsia

21.10.2016 | Health and Medicine

Stanford researchers create new special-purpose computer that may someday save us billions

21.10.2016 | Information Technology

From ancient fossils to future cars

21.10.2016 | Materials Sciences

More VideoLinks >>>