For starters the whole street network is represented as a directed graph. The most widely used algorithm is the venerable A* to find paths through the vertices of the graph, not necessarily the shortest distance but the most optimal distance given all the trade-offs you wish based on the heuristics you define. There are lots of variations of A* and today most implementations would use its faster cousin: bidirectional A* which attacks the point-to-point calculation from both ends at the same time.
Then you have Dijkstra which is used for flood searches to e.g. give the best cost back home from every vertex so you know when to turn back the search if you have a search budget.
Menger’s theorem I’ve used in order to determine whether we can create a loop back. Basically search outwards, then search back without visiting those same edges.
Tarjan to ensure we identify all subnetworks so we don’t get stuck in a disconnected island of vertices with no way out to join the wider network.
A lot of these algorithms were conceived decades ago and are still the backbone of modern routing software.
One thing that’s constantly been in the back of my mind is, since routing is a highly deterministic problem space, it doesn't seem plausible that LLMs can take this over. It seems to me that it's a good example of a tool that LLMs would call out to rather than implement themselves.
In fact, see this convo I had with @simonw wherein he had Astra generate a jogging route. It setup a whole GIS stack and took about half an hour. That seems like a boil the ocean kind of approach and I’m not sure if that’s ever going to be optimal. https://x.com/baz_shkara/status/2099118620647305630
Finding the most optimal traveling salesman problem for 20 cities by brute force will take a few universes lifetimes and you still won’t be halls way. You’ll need to compromise with heuristics but that usually leads to near optimal
But maybe I should read this to see if there's anything that applies to my current work.
IMO, it’s much more practical to thoroughly learn and understand the simpler techniques. There is often more depth to it, than you’d think.
Analogy: Many (most?) MMA matches are won with techniques you learn in the first year.
Aside: I’ve gotten much more mileage out of simple statistics in the 16 years since I graduated, than advanced algorithms.
EDIT:
IMO, theories and techniques can be easy enough to learn. Figuring out applications can be much more difficult. It requires some creativity.
This author has done nothing to deserve that scrutiny, but I can’t escape the feeling now of having to be guarded when I see a new book online with a relatively short history (spring 2026 is the earliest version of this text), as I can’t be sure it’s either “AI-enhanced” or AI-written.
I don’t like this feeling and it dampers any enthusiasm I once had for being excited about stuff like this.
That aside, if the author did write this themselves without AI, kudos to them and their acheivement!
This book aside, though, the fact that writing is no longer definitive evidence of human thought is one of the things I dislike the most about the LLM era. I very much share your sadness about that.
I vocalize this feeling I have, not because the author has done anything to warrant it, but here, in this forum, we commonly have folks saying “so what if it’s AI?”, and by bringing up these feelings we have around the industry, we can have the conversation and (hopefully) have other folks think twice about whether they would use AI to write their book.
I want to read this book and have added it to my list of things to read; and your vouching for the author does help. One underlying issue I have (that is a me problem) is that I know nothing about this particular area, and therefore know nothing about the experts in this area, so I rely on human vouching.
But also, I would like money I spend to go to people, not tokens.
The author put his name and reputation to it. If it's excellent work, it's excellent work. If it's slop, it's slop.
For at least the past 5 years, Amazon.com has been completely flooded with throwaway brand names churned out from random sequences of characters selling white-labelled products. The ones that do poorly get discarded and replaced, and the ones that find traction get to climb the rankings.
Do you think the same doesn't apply to "authors" of books, social media posts, and even academic papers in 2026? It doesn't matter if someone's staked their reputation unless their reputation is already widely known and trusted to begin with.
Just like reputation already worked. People have associations with each other. People endorse each other. Endorsements carry some transitive weight (I suppose you could use graph theory to model this). This has nothing to do with AI. Yes, Amazon is full of constantly changing "brands" with no reputation. That is different from a person or company that does have a consistent reputation that you can look up, even if you hadn't heard of them until today. Even Amazon also has e.g. Samsung or Asus if you don't want to buy AHIKJASFDIUHER.
The last time I looked into someone's complaint on HN about Chinese companies setting themselves up on Amazon with nonsense data and no way to contact them nor any theoretical method of holding them to account for misbehavior, I went to the product link the complaining comment provided and discovered that it was offered by a company whose registered place of business (listed on Amazon!) was obviously the poor owner's personal home address.
This book is presented as being written by a human. (In this case, a human I happen to know, which would add another dimension to my complaint, so let's imagine that weren't the case.) Maybe someday we'll live in a world where sticking a person's name at the top of a book doesn't carry the implication that they wrote the words in the book. That would make me sad for other reasons, but in any event, we don't live in that world right now, so for now, if you put a person's name on your book, you are claiming that that person wrote the book. If that's not true, you are lying, and like most people, I don't like being lied to.
I'm imagining something more like the way we treat movie directors. When I see Michael Bay vs. Quentin Tarantino, I don't think that those people wrote the film, or set up every camera shot in minute detail, or designed the costumes, etc. but I know that they had a hand in arranging for all of that and it will all ultimately come through with their unique stamp on it.
But regardless of whether you think your new system would be better, it's not the current system. Surely the question of whether someone is lying by putting their name on a book they didn't write can't depend on some hypothetical future change to the meaning of authorship that hasn't happened yet.
Not even an AI thing, we don't. Ghost writing has been going on for centuries.
I don't like that! I agree it's dishonest and I wish we lived in a world where having been exposed employing a ghostwriter is a disgrace no public figure can come back from. I don't like that AI has made it worse, either. At least with ghost writing there are some contexts (politicians, celebrity bios) where you might suspect it, but in most you won't.
But, we do live in that world right now.
It's not a perfect proxy, but I'm usually going to trust a domain expert over the confident idiot who constantly lies to me, hides and downplays mistakes, and flits around opposing positions like a drunken moth.
At this time, if I see a text is AI generated, I have to assume it is unsound and possibly even nefarious. There is way too much information assailing my daily life that I have no other rational choice.
the erosion of trust will be socially catastrophic.
remember a time where you might admire a photo not just for its beauty, but for the good luck and skill of the photographer who captured it?
photoshop made us skeptical about truth, but AI will simply make it hopeless to ascertain truth.
note that i use AI extensively. i am hyper aware of the way it has impacted me, my peers, and my career, and im deeply concerned about how it will impact everyone as it is increasingly made "non-optional" by the rich and greedy who stand to benefit most from it.
I wouldn't use it as a 100% infallible AI detector when the stakes are high (accusing someone of cheating) but it's very good at detecting AI generated text when you can drop large sections of text into it.
In this sense AI does not actually detract from that - so long as there IS an author associated to the book, that author can build a reputation for thoroughly reviewed and high quality textbooks. So in the end, some authors will be known for a reputation for making good books, and the use of AI should give us access to a larger quantity of books, addressing more and more niche topics, for lower costs. So, this should be a good thing for education?
I'm very much just writing my thoughts down, but curious to know if others agree or disagree with this.
> In this sense AI does not actually detract from that [...] that author can build a reputation for thoroughly reviewed and high quality textbooks.
The issue is a lot of the AI generated books out there aren't carefully reviewed and it being AI written is an early sign it's crap at the moment, and it's expensive cognitively to build a list of "trusted authors" or to know when searching if you're finding true reviews by people who can meaningfully evaluate the content of the book or if you hit an AstroTurf post fluffing the author.
The other indicator and thing that puts at least myself off is that if the author used AI significantly in the process they didn't care enough about writing it before to put the real human effort into writing it so the chances it's worth spending my real human time reading is low.
I think there's more, we just take it for granted because it's usually included. Imagine a teacher--perhaps a whimsical one in a Roald Dahl story--who is always very accurate and correct. However, somehow they always present things in a way that cripples students' future progress and understanding.
Most human communication involves some level of simulating the mind you expect was/will-be at the other end. This aspect becomes extra-important when teaching, because teaching about trying to change how that student-mind operates.
So the facts being imparted are secondary, and in many cases carefully incorrect facts must be used before you can introduce better ones.
Many books pre-ai were garbage but not at the rate they could be today. If anything people operate on greater discretion now than in the past because even the worst garbage still had a non-trivial barrier to entry, either sitting down to regurgitate your own garbage or paying someone to make some garbage for you.
There's also some historic precedence of this, the rise of Photoshop/CG and digital manipulation certainly led to a "is this photo real" to similar effect despite manipulations going back to the origins of photography. That acute concern was not as prevalent in my mind before editing became common and accessible.
Quite frankly this is.. fucking terrible? Even worse, the end of something for humanity..?
Where I've landed -- once I get away from the distaste for load-bearing or a comment mentioning "spine" -- is that if the idea pushes me forward, challenges me towards improving, or otherwise informs, I'm okay with AI assisted writing.
I'm not okay with formulaic garbled nonsense, that annoys me!
I think we're quickly getting to a point where AI is going to be able to do a better job teaching things than humans can (especially stuff with heavy associations with paper/screens, like programming and math). AI can augment for personal styles and spin up whole entire educational widgets on demand. Human's can't scale like that.
I think there is some worth in having someone knowledgeable using AI to generate educational material, although it will be in my opinion, of less use than if that knowledgeable person wrote the material by hand.
For example, many professors in universities have started generating slides or even assignments using AI. A knowledgeable teacher who cares about their students outcomes can generate better material.
Can we not do this? I understand your sentiment, but ... can we not do this?
Also, saw your comment response, I do feel this very same guarding and unfortunately my instinct is to assume the content is AI, which is a disservice to all the people who are putting their hard effort into putting out quality things.
For sure it was less to review, less options but still.
So what did you use? I used things like Reviews, skimming through, getting a referal through a blog or hn and buying from reputational sources.
HN is a filter. Same as all the other things we have.
Like is there a concrete issue with the book you have?
But who reviews the reviewers?
1. AI generated text works off of whatever model it came from, whatever prompt was used, and probabilities. It’s been described as a “next token predictor” and that, for the purposes of this answer, is how I’m describing it as well. First problem: it’s only as good as the above.
2. Because of the above, its accuracy relies on probabilities. It can confidently give me wrong information, and as someone who would read this book to learn a topic I don't already know, I have no frame of reference to know whether I’m being fed accurate information.
3. Since it greatly speeds up the time it takes to physically write material, there is a possibility the author didn’t closely vet the information provided by the LLM as a next token predictor. That means it could be wrong in subtle ways, and the only way for me to know is to rely on knowledge I don’t have.
4. Had AI not been used, I could conceivably go on the past work of the author, rely on the person who has the expertise who wrote the forward, or the fact that physically writing a book takes prohibitively long enough that the dopamine from having written a book doesn’t outweigh the amount of time it takes, and if you are going to take months to years to write a book, you’re going to not want that effort to be in vain. You’re going to do your diligence and not just “wing it”.
AI makes it relatively trivial to appear knowledgeable and to get that dopamine rush from saying “I’m an author” and appearing to be an expert in a field without being an expert in a field. For some, that temptation is too great and there’s no way to know without the passage of time. Time for folks to review the book who know the subject matter. Time for reviews. Time for folks to put signs up that say “don’t trust this material.” In the meantime we still have that content out there, further infecting new AI models and people into believing it’s accurate.
That’s why the use of AI is dangerous, and is especially dangeorus without disclosure.
Well guided is a qualifier that matters.
I have observed that models are not able to effectively come down to a human level. They are mediocre at approximating what a first-time reader would want to know. If you will forgive the anthropomorphization, they are not very empathetic. In this book for example, the author pauses the flow of thought with countless little anecdotes, anticipating where the reader might have a question or want to know more.
Of course, a well-guided AI is capable of anything a human is capable of. But is that not tautological?
As well, if people were a bit less anti-AI then maybe we can get disclaimers that things are written by AI that don't immediately torpedo any value the writing has.
Tangent: I use AI for code, but I've had to ban it from writing readmes and doc comments; the AI models I've used produce text I'm unable to parse, and assume my readers would not be able to either.
I don't understand why HN cannot ever say the first sentence without the second one.
Most people agree that using AI for research or finding better words is fine, but then can't upvote or have a meaningful conversation because of the performative politics and wild delusions about a scifi future.
Dude, all we have with LLMs is an NLP search engine. Get over it. It's been around half a decade of this nonsense. There is no "step change". There is no "hockey stick" curve. The models have not "dramatically improved compared to last year" regardless of what year it currently is. There is no big bad overlord coming for you. Nobody is getting replaced by AI. Even frontier AI can't replace local AI. It's just the logical next step towards better search that assumes you want the "I'm feeling lucky" button a little too often.
[1] https://en.wikipedia.org/wiki/PageRank
A good graph theory course abstracts away the details of code and pursues the goal of understanding how many problems can be expressed concisely and clearly through graphs.
A good leetcode practice ... honestly just hones how patient you are in debugging and memorising various code patterns.
If you want to pursue money, it's almost always better to pursue leetcode exclusively
Graph theory and algorithm engineering overlap a great deal. And not only in the directly graph theoretic terms like BFS, Dijkstra, Flow, etc, but also in that you need a good grasp of greedy algorithms, dynamic programming, divide and conquer, and several other general techniques.
Kind of like how being good at relational-databases and SQL is different than being good at coding up B-tree implementations.
The advice is sound -- if you want money focus on the flashy buzzword thing, not the actually useful thing.
In a hardware manufacturing setting, particularly a new or "garage" sort of shop doing lots of new business, you quickly get into a nightmare scenario of "Too Many Configurations" running headfirst into the problem of "People Are Buying Too Much of Our Stuff". As a garage shop you can do OK making five or six units of all kinds, but once the orders for 1000, 10000 start coming in, you will be torpedoed by the complexity of keeping all those lines operational. Eventually you'll screw something up, and get dinged or even blacklisted (a big deal in Defense).
But it's a problem that can be steered around by applying some graph theory to the parts data system. Some PDMs actually do this natively - Oleg Shilovitsky's OpenBOM; Yoann Maingon's Ganister, both smart guys buy their stuff! - but this network theory can be used as a reporting layer on top of any big dumb PDM.
Examples include:
(Asciidoc table from a previous slide I've used, sorry)
|===
| Method | Primary Use
| In-degree centrality | Shared/high-risk components
| Out-degree centrality | Complex assemblies
| Betweenness centrality | Change risk
| Closeness centrality | Architectural centrality
| PageRank | Strategic component
| Degree distribution | Architecture health / power law check
| Connected components | Find orphans
| Shortest path / diameter | BOM depth, lineage distance
| Clustering coefficient | Modularity vs. coupling
| Community detection | Platform map, family boundaries
| Ego network | "Minimum Safe Distance" of a change impact
| Jaccard similarity | Variant/redundancy
| Structural holes | "Bridge" component(s)
| Topological sort | Flat assembly sequence
| Longest path | Maximum BOM depth
| Transitive closure | Full ancestor/descendant sets
| Treewidth | Overall architectural complexity score
|===
Graphs in general are high dimensional structures and don't lend themselves to 2D projections. That is not a problem with coding the layouting algorithm. There simply is no good geometric arrangement for most graphs / networks because they are not planar [0], or even close to it (with few intersections).
I would even say that "Everyone Should Start Doing Graph Theory", but it's only my opinion of course. Take it or leave it.
I remember to this day the exact location I was when being introduced to construct hypercubes, to the exact bench in our uni cafeteria. It changed my understanding of multidimensionality completely.
Related HN thread: https://news.ycombinator.com/item?id=17745779
AHH. Definition 1.4 and the questions after did it. It went from "Tracking all" to "I don't understand how this follows at all, and this makes no sense to me" 1.3b is a graph, not a union of two graphs?. What are the "two graphs"? What is this operator-like algebra, and what does it have to do with the rest of the definition or the text before and after it? A question about the complement which was never defined? Why are we probably agreeing that {1, 2} contain 3?
Update: Better phrasing I can understand:
"Definition 1.4. The union of two graphs G and H, denoted <>, is a single graph containing all vertices and edges from both. If G and H share no vertices in common, <> is a disjoint union."
For 1.5, I had no idea what the written definition meant, but this does: ``` Definition 1.5. The complement of graph G is the one that has the same vertices, two vertices are connected in G_complement if and only if they are not connected in G.
There are plenty of ways to get a copy.
(Edit) But I understand that goal of a book can be completely different. So it's just problem of my expectations.
Yes, but I think it's important to state that it's only reliable for things that are very well known and extensively written about.
And for the bleeding edge part: My godchild wanted to know the name of a Pokémon from his licensed shirt. One of the first ones, found in every training set. Couldn't get it right, was certain it was the wrong one.
how did you even ask an AI this question? Took a picture of the shirt, uploaded it, and asked the AI what it was? That's a different class of problem than "answer this graph theory question and include your references: <paste text here>"
You don't ask for proofs to print them out, put them in your drawer, and brag around that you own the proofs for these exercises.
You ask Claude for proofs to help your understanding. Understanding is the exact same activity as verifying.
(Assuming it's a proof or something - if it's just a number - oh well).
More and more it feels like as humans we are re-entering the pre 1700s era where most humans never learnt any technical knowledge, circa they never needed it.
The LLM boosters will claim, this is good and fine, LLMs will create an age of miracles and we will climb the kardashev scale or whatever other nonsense. I don’t think that will happen, I’m like 99% sure we won’t even cure cancer. We’re just making large swathes of intellectual work that we invented since the 1700s to now redundant for some reason and hoping that’s a better future, we are liberated from the “toils of thinking”. Well humanity has lived for 1000s of years without thinking of any of this stuff, so we’ll be fine but I suspect the world was richer when we did think about all this.
Please prove me wrong.