What Rules in Your Business are Just Habits?

Consider you own a factory that needs to distribute goods to all customers, or that you are trying to get information to travel swiftly across geographically-dispersed teams. How would you do it?

Engineers, over decades, have dealt with such a problem by always proceeding next to the closest option (node), whilst maintaining a running list of who is closest so they don’t make the wrong choice. While this is a solid fool-proof way to do so, creating and maintaining an ordered list of every possible node – especially when there can be thousands of small moving parts – is often rather time-consuming and difficult.

A recent publication by a group of researchers at Tsinghua University, Stanford University and the Max Planck Institute of Informatics beats this long-held time bound on this problem with aplomb, creating an algorithm that can solve it considerably faster than the previously-believed optimal. And that too in a way that does not require keeping the data perfectly in line with one another.

This discovery is not a slight change. It is a sea-shift challenging one of the long-standing limiting beliefs within the field of computer science. It is also a great lesson to managers and students alike: what you think are musts, sometimes may only be habits to be overcome.

Out with the Old

The classic approach is fool-proof because it is uber-cautious: it makes an orderly choice –  the closest surrounding unexplored area – and updates a list so it is never inaccurate. That security lies in maintaining a full book of distances as does a planner who refuses an order till he has ranked all the deliveries and only then sends out a truck. The unconscious cost of the whole process is that highly tedious ranking step.

The novelty approach – don’t attempt to order everything.

The crux of the wisdom in the paper is deceptively straightforward: you do not need an ideal world order to get optimal paths. Rather, the researchers combine two more established approaches – the painstaking, system-wide approach and a more free-wheeling, locally-updated approach – with a trick that discovers points of leverage that make a difference. By chunking the problem into smaller pieces, and putting effort where it matters, they reduce the massive work involved in maintaining a highly methodical sorted list.

The technical approach identifies a limited number of “pivot” points, whose choices lead to a majority of other consequences. It does not analyze everything in detail, but rather targets such pivots and solves much of the issue within a far shorter time. In our case of deliveries: locate who the pivots are, the small set of customers, suppliers or groups whose actions have a snowball effect, and do something about that instead of waiting to see a full, rounded out picture.

While it makes for a neat technical finding, the business lesson is also clear: A way of doing something will often become sacrosanct to an organization just because it has almost always been so. The researchers assumed the same with the long-term sorting requirement which they assumed was a law – only to discover it wasn’t. Circling back, it’s a useful nudge for all of us – are your “musts” true constraints or just habits? 

One practical mindset shift

Launching a product? Begin testing with a small number of customer groups with the greatest likelihood to move the market – not each potential niche.

Fixing operations? Patch only that which acts as a roadblock to others instead of attempting to rewrite the whole process.

Investing in a change program? Run fast, small pilots in high-leverage areas; once the pivot points do what they should, scale.

Perfection is seductive, but sometimes real strength lies in what not to make perfect. The new paper demonstrates that accepting partial order and specialising effort where it multiplies will make you faster and (in practice) equally correct.

No more worshipping of complete tidy lists. Start hunting pivots, and keep moving.

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Technical note

The paper behind this idea is “Breaking the Sorting Barrier for Directed Single-Source Shortest Paths” by Ran Duan, Jiayi Mao, Xiao Mao, Xinkai Shu and Longhui Yin (July 2025). The authors give a deterministic algorithm that runs in roughly O(m · log^(2/3) n) time for directed graphs with non-negative edge weights — where n is the number of nodes and m the number of edges.

In plain terms: for many sparse networks this is provably faster than the long-standing Dijkstra approach (which runs in about O(m + n log n) time), showing that the old “sorting everything” habit wasn’t as unavoidable as people thought. The speedup comes from combining careful local updates with a divide-and-conquer way to find a few high-impact “pivot” nodes, so you avoid doing expensive global ordering work everywhere.

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Find the paper here.

Find coverage from Quanta Magazine here.