Computer scientists have written a network flow algorithm that computes almost as fast as is mathematically possible. This algorithm computes the maximum traffic flow with minimum transport costs for any type of network. It thus solves a key question in theoretical computer science.
The superfast algorithm also lays the foundation for efficiently computing very large and dynamically changing networks in the future.
Kyng's approach eliminates this problem: using his algorithm, computing time and network size increase at the same rate -- a bit like going on a hike and constantly keeping up the same pace however steep the path gets. A glance at the raw figures shows just how far we have come: until the turn of the millennium, no algorithm managed to compute faster thanstands for the number of connections in a network that the computer has to calculate, and just reading the network data once takes.
Specifically, these algorithms identify the shortest routes in networks where connections are added or deleted. In real-world traffic networks, examples of such changes in Switzerland include the complete closure and then partial reopening of the Gotthard Base Tunnel in the months since summer 2023, or the recent landslide that destroyed part of the A13 motorway, which is the main alternative route to the Gotthard Road Tunnel.
Kyng's team has now tied together the respective advantages of these two strategies in order to create a radical new combined approach."Our approach is based on many small, efficient and low-cost computational steps, which -- taken together -- are much faster than a few large ones," says Maximilian Probst Gutenberg, a lecturer and member of Kyng's group, who played a key role in developing the almost-linear-time algorithms.
Yet laying the foundations for solving very large problems that couldn't previously be computed efficiently is only one benefit of these significantly faster flow algorithms -- because they also change the way in which computers calculate complex tasks in the first place.
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