“This is a result I have wanted all my career,” said David Williamson of Cornell University, who has been studying the traveling salesperson problem since the 1980s.
The traveling salesperson problem is one of a handful of foundational problems that theoretical computer scientists turn to again and again to test the limits of efficient computation. The new result “is the first step towards showing that the frontiers of efficient computation are in fact better than what we thought,” Williamson said.
While there is probably no efficient method that always finds the shortest trip, it is possible to find something almost as good: the shortest tree connecting all the cities, meaning a network of connections (or “edges”) with no closed loops. Christofides’ algorithm uses this tree as the backbone for a round-trip tour, adding extra edges to convert it into a round trip.
Any round-trip route must have an even number of edges into each city, since every arrival is followed by a departure. It turns out that the reverse is also true — if every city in a network has an even number of connections then the edges of the network must trace a round trip.
The shortest tree connecting all the cities lacks this evenness property, since any city at the end of a branch has just one connection to another city. So to turn the shortest tree into a round trip, Christofides (who died last year) found the best way to connect pairs of cities that have odd numbers of edges. Then he proved that the resulting round trip will never be more than 50% longer than the best possible round trip.
In doing so, he devised perhaps the most famous approximation algorithm in theoretical computer science — one that usually forms the first example in
Digital Strategy Lands MSA Safety Special Recognition by IR Magazine; Company Receives 2020 Best Investor Relations Website Award
PITTSBURGH, Sept. 28, 2020 /PRNewswire/ — Along with global safety equipment manufacturer MSA Safety Incorporated’s (NYSE: MSA) mission of protecting lives, staying agile and responsive to customer needs has been an unwavering focus for more than a century. Today, the company announced that their efforts to leverage digital technologies to engage with the investor community were recently recognized by IR Magazine with the 2020 Best Investor Relations (IR) Website award. The award was presented on September 16 as part of a virtual awards ceremony held by IR Magazine. Elyse Lorenzato, MSA Director of Investor Relations, accepted the award on behalf of the company.
Based on feedback from analysts, investors and a panel of judges, IR Magazine evaluates companies across 27 categories. The Best IR Website category recognizes best-in-class websites that deliver “a top-notch customer experience, engaging content that meets analysts’ and investors’ needs, and provides a truly interactive experience.”
MSA’s custom-branded IR site provides engaging content while seamlessly facilitating the investment research process. The site contains best-in-class features based on a mobile-responsive design, automatically adjusting to the size of a user’s device without sacrificing content or functionality. These features include a new horizontal navigation menu; a featured resources “quick-links” section to display recent presentations and materials; social media gateways; multi-media landing pages for investor events; video content highlighting strategy and technology; quarterly infographics; ESG reports; and streamlined home-page content groupings to improve navigation through the site.
“I’m very proud of the cross-functional team that designed and launched the investor relations website and their success in bringing innovation to all aspects of MSA’s business,” said Ken Krause, MSA Senior Vice President, Chief Financial Officer and Treasurer. “Our approach to investor relations has evolved concurrently as MSA has grown over the years. As part of that journey, we’ve taken the opportunity to