Stories with Tag Graph Theory

• Shortest-possible walking tour to 81,998 bars in South Korea

  permalink

  Posted: 2025-04-24 00:20:40

  Verbose tl;dr

  A researcher has calculated the shortest possible walking tour visiting all 81,998 bars in South Korea, a journey spanning approximately 115,116 kilometers. This massive traveling salesman problem (TSP) solution, while theoretically interesting, is practically infeasible. The route was computed using Concorde, a specialized TSP solver, and relies on road network data and bar locations extracted from OpenStreetMap. The resulting tour, visualized on the linked webpage, demonstrates the power of sophisticated algorithms to tackle complex optimization challenges, even if the application itself is whimsical.

  This webpage meticulously documents the computational journey undertaken to devise a remarkably efficient walking tour encompassing a staggering 81,998 bars located across the entirety of South Korea. The central challenge, framed as a Traveling Salesperson Problem (TSP), involves determining the shortest possible route that visits each bar precisely once and returns to the starting point. Given the immense scale of this particular problem, with nearly 82,000 distinct locations to consider, arriving at an optimal solution presents a formidable computational hurdle.

  The author employs sophisticated optimization techniques, specifically a refined implementation of the Lin-Kernighan heuristic, to tackle this complex task. The Lin-Kernighan heuristic is an iterative algorithm that systematically improves an initial tour by identifying and swapping segments to progressively reduce the overall distance. Due to the sheer magnitude of the problem, the computations were distributed across a network of computers, leveraging their combined processing power to gradually refine the solution over an extended period.

  The resulting tour, meticulously detailed on the webpage, represents an exceptionally efficient traversal of these numerous establishments. The author provides various visualizations of the tour, including interactive maps and downloadable data files, allowing for in-depth exploration of the generated route. Furthermore, the webpage offers insights into the computational methodology employed, highlighting the challenges encountered and the strategies adopted to overcome them. The magnitude of the problem and the impressive optimization achieved underscore the power and applicability of advanced algorithmic techniques in tackling real-world logistical challenges, albeit in this instance, applied to a rather unconventional, yet fascinating, scenario. While the practical implications of visiting nearly 82,000 bars are perhaps debatable, the project serves as a compelling demonstration of the capabilities of modern optimization algorithms when applied to exceptionally large datasets.

  • traveling salesman problem
  • TSP
  • optimization
  • Graph Theory
  • algorithms
  • South Korea
  • walking tour
  • bars
  • route planning
  • shortest path
  • combinatorial optimization
  • mathematics
  • Geography
  • travel

  Summary of Comments ( 122 )
  https://news.ycombinator.com/item?id=43778105

  Verbose tl;dr

  HN commenters were impressed by the scale of the traveling salesman problem solved, with one noting it's the largest road network TSP solution ever found. Several discussed the practical applications, questioning the real-world usefulness given factors like bar opening/closing times and the impracticality of actually completing such a tour. The algorithm used, Concorde, was also a topic of discussion, with some explaining its workings and limitations. Some users highlighted potential issues with the data, specifically questioning whether all locations were truly accessible by road, particularly those on islands. Finally, a few users humorously imagined actually attempting the tour, calculating the time required, and referencing other enormous computational problems.

  The Hacker News post titled "Shortest-possible walking tour to 81,998 bars in South Korea" sparked a discussion with a moderate number of comments, primarily focusing on the computational aspects of solving the Traveling Salesperson Problem (TSP) at such a large scale. Several commenters expressed fascination with the scale of the problem and the optimization techniques employed.

  One commenter highlighted the use of Concorde, a specialized TSP solver known for its efficiency, and questioned whether the solution found was truly optimal or just a very good approximation. They also raised the practical considerations of such a tour, noting the impracticality of actually undertaking it. This sparked a small side discussion about the definition of "optimal" in the context of TSP solvers and the computational resources required to guarantee true optimality for very large datasets.

  Another commenter delved into the specifics of the algorithm used, mentioning the Lin-Kernighan heuristic as a key component of Concorde's approach. They explained how this heuristic iteratively improves a tour by swapping edges to find shorter paths. The discussion then touched upon the concept of "tour length," distinguishing between Euclidean distance and actual travel distance, with an acknowledgement that the solution likely focuses on abstract distance rather than real-world walkability.

  There was also a brief exchange about the data source for the bar locations, with speculation about the use of OpenStreetMap (OSM) or similar databases. This led to a comment about the potential issues with data accuracy and completeness, particularly in densely populated areas.

  A few comments offered humorous takes on the premise, imagining the physical challenges of completing such a tour and the potential toll on one's liver.

  Overall, the comments section reflects a mix of technical appreciation for the computational feat, practical considerations about the real-world implications, and lighthearted amusement at the absurdity of the concept. No one seemed to be planning an 82,000-bar pub crawl anytime soon, but the problem clearly captured the imagination of several commenters.

• Things I would have told myself before building an autorouter

  permalink

  Posted: 2025-03-28 00:38:53

  Verbose tl;dr

  Building an autorouter is significantly more complex than it initially appears. It's crucial to narrow the scope drastically, focusing on a specific problem subset like single-layer PCBs or a particular routing style. Thorough upfront research and experimentation with existing tools and algorithms is essential, as is a deep understanding of graph theory and computational geometry. Be prepared for substantial debugging and optimization, especially around performance bottlenecks, and recognize the importance of iterative development with constant testing and feedback. Don't underestimate the value of visualization for both debugging and user interaction, and choose your data structures and algorithms wisely with future scalability in mind. Finally, recognize that perfect routing is often computationally intractable, so aim for "good enough" solutions and prioritize practical usability.

  The author of "13 Things I Would Have Told Myself Before Building an Autorouter" reflects on the arduous journey of developing an autorouting tool, offering a comprehensive list of lessons learned through experience. He emphasizes the immense complexity inherent in such a project, cautioning against underestimating the scope. The initial naive assumption that existing algorithms would suffice proved drastically incorrect, leading to a deeper appreciation for the nuances and intricacies of routing.

  He stresses the critical importance of meticulously defining the problem and establishing clear objectives before diving into development. Without a precise understanding of the constraints and desired outcomes, the process can quickly become unwieldy. Furthermore, he underscores the value of iterative development and incremental progress, advocating for a phased approach with continuous testing and refinement rather than striving for an all-encompassing solution from the outset.

  The author details the challenges of data representation, highlighting the significance of choosing an appropriate data structure that can efficiently handle the vast amounts of information involved in routing. He also emphasizes the need for robust error handling and debugging strategies, given the inevitability of encountering unexpected issues and edge cases. Performance optimization becomes a paramount concern, requiring careful consideration of algorithms and data structures to ensure responsiveness and scalability.

  A key takeaway is the realization that achieving perfection is an unrealistic goal in autorouting. Instead, the focus should shift towards finding a balance between performance, accuracy, and practicality. The author learned the hard way that attempting to cater to every possible scenario can lead to an overly complex and ultimately less effective solution.

  He further discusses the importance of understanding the specific requirements of the target application. Generic autorouting algorithms often fall short when applied to specialized domains, necessitating customization and adaptation. He also advises against neglecting the user interface and user experience, recognizing that even the most powerful autorouting engine is useless if it's not accessible and intuitive to use. Finally, the author emphasizes the continuous nature of development, acknowledging that an autorouter is never truly "finished" and requires ongoing maintenance, updates, and improvements to stay relevant and effective.

  • autorouting
  • PCB Design
  • electronic design automation
  • EDA
  • Software Development
  • lessons learned
  • algorithms
  • Graph Theory
  • Routing
  • optimization
  • Computer Science
  • Engineering

  Summary of Comments ( 76 )
  https://news.ycombinator.com/item?id=43499992

  Verbose tl;dr

  Hacker News users generally praised the author's transparency and the article's practical advice for aspiring software developers. Several commenters highlighted the importance of focusing on a specific niche and iterating quickly based on user feedback, echoing the author's own experience. Some discussed the challenges of marketing and the importance of understanding the target audience. Others appreciated the author's honesty about the struggles of building a business, including the financial and emotional toll. A few commenters also offered technical insights related to autorouting and pathfinding algorithms. Overall, the comments reflect a positive reception to the article's pragmatic and relatable approach to software development and entrepreneurship.

  The Hacker News post "Things I would have told myself before building an autorouter" sparked a brief but interesting discussion with a few insightful comments. No one seemed to directly challenge the author's points from the original blog post, but rather expanded upon them or offered related anecdotes and perspectives.

  One commenter highlighted the importance of understanding the specific problem domain before diving into a complex project like autorouting. They mentioned that often, 80% of the routes are "trivial" and easily solved, while the remaining 20% present the real challenge. This commenter emphasized focusing on that difficult 20% and understanding its nuances, rather than getting bogged down in optimizing for the easy cases. They provided an example from their experience with PCB routing, where certain high-speed signals required specialized handling and couldn't be treated generically.

  Another commenter echoed this sentiment by discussing the "long tail" of edge cases in software development. They agreed that optimizing for the common scenarios is often straightforward, but dealing with the unusual or unexpected situations is where the real difficulty lies. This reinforces the idea of needing deep domain expertise to anticipate and handle these less frequent but crucial scenarios in autorouting.

  A third comment shifted the focus slightly to the importance of iterative development and testing. They described a similar project where they initially aimed for a perfect solution but later realized the value of incremental improvements. This commenter advocated for starting with a simple, working system and gradually enhancing it based on real-world feedback and testing. They suggested that this approach allows for faster learning and adaptation, ultimately leading to a more robust and practical solution.

  Finally, one commenter briefly mentioned the concept of constraint solvers and their potential relevance to autorouting problems. While they didn't elaborate extensively, this comment hinted at alternative approaches and tools that might be valuable in this domain.

  Overall, the comments on Hacker News provided valuable additions to the original blog post by emphasizing the importance of understanding the problem domain, focusing on edge cases, and adopting an iterative development approach. They offered practical insights and relatable experiences, further enriching the discussion around the challenges of building an autorouter.

• Specializing Python with E-Graphs

  permalink

  Posted: 2025-03-18 12:58:40

  Verbose tl;dr

  The blog post explores using e-graphs, a data structure representing equivalent expressions, to create domain-specific languages (DSLs) within Python. By combining e-graphs with pattern matching and rewrite rules, users can define custom operations and optimizations tailored to their needs. The post introduces Egglog, a Python library built on this principle, demonstrating how it allows users to represent and manipulate mathematical expressions symbolically, perform automatic simplification, and even derive symbolic gradients. This approach bridges the gap between the flexibility of Python and the performance of specialized DSLs, enabling rapid prototyping and efficient execution of complex computations.

  The blog post "Specializing Python with E-Graphs" by Alex Warth explores a novel approach to optimizing Python code using a technique called equality saturation via e-graphs. The core idea revolves around representing a program's computational steps as a graph structure, specifically an e-graph, which allows for the efficient exploration and application of rewrite rules to simplify and optimize the program's logic.

  Traditional compiler optimizations often operate on a relatively low level, focusing on individual instructions or basic blocks of code. E-graphs, however, enable optimization at a higher level of abstraction. By representing the program's semantics as a graph, where nodes represent expressions and edges represent equalities between them, e-graphs can capture and exploit complex mathematical relationships within the code.

  The author uses the Egglog system, built atop the egg e-graph library, to demonstrate this concept within Python. Egglog allows users to define rewrite rules, expressed as logical equivalences, which are then applied to the e-graph representation of the Python code. As the e-graph is saturated with these equalities, equivalent expressions are merged, leading to a simplified and potentially more efficient representation of the original program. This simplification process can automatically discover and apply optimizations that might be difficult or tedious to perform manually.

  The blog post provides concrete examples of how e-graph rewriting can be used for various optimization tasks, including constant folding, common subexpression elimination, and even more complex transformations like converting recursive functions into iterative ones. A key advantage highlighted is the ability to define domain-specific rewrite rules, enabling targeted optimizations tailored to particular applications or algorithms.

  The post further delves into the mechanics of e-graph rewriting, explaining how the system efficiently maintains the graph structure and applies rewrite rules until saturation is reached. It also touches on the challenges associated with this approach, such as the potential for exponential growth of the e-graph in certain cases, and discusses strategies for mitigating these issues.

  Finally, the author outlines future directions for this research, suggesting potential applications in areas like automatic differentiation and program synthesis. The overall message is that e-graph rewriting offers a powerful and flexible new paradigm for program optimization, potentially enabling significant performance improvements and automation of complex optimization tasks within Python and other languages.

  • Python
  • E-Graphs
  • Program Synthesis
  • Symbolic Programming
  • Term Rewriting
  • code optimization
  • compiler optimization
  • program analysis
  • Graph Theory
  • egglog

  Summary of Comments ( 0 )
  https://news.ycombinator.com/item?id=43398908

  Verbose tl;dr

  HN commenters generally expressed interest in Egglog and its potential. Several questioned its practicality for larger, real-world Python programs due to performance concerns and the potential difficulty of defining rules for complex codebases. Some highlighted the project's novelty and the cleverness of using e-graphs for optimization, drawing comparisons to other symbolic execution and program synthesis techniques. A few commenters also inquired about specific features, such as handling side effects and integration with existing Python tooling. There was also discussion around potential applications beyond optimization, including program analysis and verification. Overall, the sentiment was cautiously optimistic, acknowledging the early stage of the project but intrigued by its innovative approach.

  The Hacker News post titled "Specializing Python with E-Graphs" (linking to https://vectorfold.studio/blog/egglog) generated a modest amount of discussion, with a handful of comments focusing on the technical aspects and potential applications of the Egglog system.

  One commenter expressed excitement about the project, viewing it as a powerful tool for symbolic computation and program synthesis, particularly for tasks involving constraint solving and program optimization. They highlighted the potential for combining Egglog with other tools like SMT solvers and speculated about its usefulness in domains like robotics and compiler design.

  Another comment focused on the performance characteristics of Egglog, questioning the efficiency of using Python as the foundation for such a system. They suggested that a language with more predictable performance, or even a custom virtual machine, might be a better choice for performance-critical applications. This concern sparked a brief discussion about the trade-offs between ease of use and performance, with another user pointing out that Python's extensive library ecosystem makes it an attractive platform for rapid prototyping and experimentation, even if it comes at a cost in performance.

  One user discussed the applicability of Egglog in formal verification, wondering if it could be used to prove properties of programs or verify the correctness of hardware designs. They pointed to the growing interest in formal methods and suggested that tools like Egglog could play a crucial role in making formal verification more accessible to developers.

  Another commenter made a connection between Egglog and relational programming paradigms, such as Datalog and Prolog. They discussed the potential benefits of using a declarative approach for expressing computations and how Egglog's e-graph-based rewriting system could offer advantages in terms of expressiveness and efficiency compared to traditional relational systems.

  Finally, one user expressed a desire for more detailed examples and tutorials demonstrating the practical use of Egglog. They suggested that concrete examples, especially those relevant to specific application domains, would be helpful in understanding the capabilities and limitations of the system and in attracting a wider audience.

  Overall, the comments reflect a generally positive sentiment towards Egglog, with many commenters recognizing its potential for various applications. However, there were also some practical concerns raised about performance and the need for more comprehensive documentation and examples.

• A Gentle Introduction to Graph Neural Networks

  permalink

  Posted: 2024-12-20 04:10:42

  Verbose tl;dr

  Graph Neural Networks (GNNs) are a specialized type of neural network designed to work with graph-structured data. They learn representations of nodes and edges by iteratively aggregating information from their neighbors. This aggregation process, often using message passing, allows GNNs to capture the relationships and dependencies within the graph. By combining learned node representations, GNNs can also perform tasks at the graph level. The flexibility of GNNs allows their application in various domains, including social networks, chemistry, and recommendation systems, where data naturally exists in graph form. Their ability to capture both local and global structural information makes them powerful tools for graph analysis and prediction.

  This Distill publication provides a comprehensive yet accessible introduction to Graph Neural Networks (GNNs), meticulously explaining their underlying principles, mechanisms, and potential applications. The article begins by establishing the significance of graphs as a powerful data structure capable of representing complex relationships between entities, ranging from social networks and molecular structures to knowledge bases and recommendation systems. It underscores the limitations of traditional deep learning models, such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), which struggle to effectively process the irregular and non-sequential nature of graph data.

  The core concept of GNNs, as elucidated in the article, revolves around the aggregation of information from neighboring nodes to generate meaningful representations for each node within the graph. This process is achieved through iterative message passing, where nodes exchange information with their immediate neighbors and update their own representations based on the aggregated information received. The article meticulously breaks down this message passing process, detailing how node features are transformed and combined using learnable parameters, effectively capturing the structural dependencies within the graph.

  Different types of GNN architectures are explored, including Graph Convolutional Networks (GCNs), GraphSAGE, and GATs (Graph Attention Networks). GCNs utilize a localized convolution operation to aggregate information from neighboring nodes, while GraphSAGE introduces a sampling strategy to improve scalability for large graphs. GATs incorporate an attention mechanism, allowing the network to assign different weights to neighboring nodes based on their relevance, thereby capturing more nuanced relationships within the graph.

  The article provides clear visualizations and interactive demonstrations to facilitate understanding of the complex mathematical operations involved in GNNs. It also delves into the practical aspects of implementing GNNs, including how to represent graph data, choose appropriate aggregation functions, and select suitable loss functions for various downstream tasks.

  Furthermore, the article discusses different types of graph tasks that GNNs can effectively address. These include node-level tasks, such as node classification, where the goal is to predict the label of each individual node; edge-level tasks, such as link prediction, where the objective is to predict the existence or absence of edges between nodes; and graph-level tasks, such as graph classification, where the aim is to categorize entire graphs based on their structure and node features. Specific examples are provided for each task, illustrating the versatility and applicability of GNNs in diverse domains.

  Finally, the article concludes by highlighting the ongoing research and future directions in the field of GNNs, touching upon topics such as scalability, explainability, and the development of more expressive and powerful GNN architectures. It emphasizes the growing importance of GNNs as a crucial tool for tackling complex real-world problems involving relational data and underscores the vast potential of this rapidly evolving field.

  • Graph Neural Networks
  • GNNs
  • Graph Representation Learning
  • deep learning
  • machine learning
  • neural networks
  • Graphs
  • Introduction
  • Tutorial
  • Distill.pub
  • Visualization
  • Graph Theory
  • Network Analysis
  • AI
  • artificial intelligence
  • Data Science

  Summary of Comments ( 33 )
  https://news.ycombinator.com/item?id=42468214

  Verbose tl;dr

  HN users generally praised the article for its clarity and helpful visualizations, particularly for beginners to Graph Neural Networks (GNNs). Several commenters discussed the practical applications of GNNs, mentioning drug discovery, social networks, and recommendation systems. Some pointed out the limitations of the article's scope, noting that it doesn't cover more advanced GNN architectures or specific implementation details. One user highlighted the importance of understanding the underlying mathematical concepts, while others appreciated the intuitive explanations provided. The potential for GNNs in various fields and the accessibility of the introductory article were recurring themes.

  The Hacker News post titled "A Gentle Introduction to Graph Neural Networks" linking to a Distill.pub article has generated several comments discussing various aspects of Graph Neural Networks (GNNs).

  Several commenters praise the Distill article for its clarity and accessibility. One user appreciates its gentle introduction, highlighting how it effectively explains the core concepts without overwhelming the reader with complex mathematics. Another commenter specifically mentions the helpful visualizations, stating that they significantly aid in understanding the mechanisms of GNNs. The interactive nature of the article is also lauded, with users pointing out how the ability to manipulate and experiment with the visualizations enhances comprehension and provides a deeper, more intuitive grasp of the subject matter.

  The discussion also delves into the practical applications and limitations of GNNs. One commenter mentions their use in drug discovery and material science, emphasizing the potential of GNNs to revolutionize these fields. Another user raises concerns about the computational cost of training large GNNs, particularly with complex graph structures, acknowledging the challenges in scaling these models for real-world applications. This concern sparks further discussion about potential optimization strategies and the need for more efficient algorithms.

  Some comments focus on specific aspects of the GNN architecture and training process. One commenter questions the effectiveness of message passing in certain scenarios, prompting a discussion about alternative approaches and the limitations of the message-passing paradigm. Another user inquires about the choice of activation functions and their impact on the performance of GNNs. This leads to a brief exchange about the trade-offs between different activation functions and the importance of selecting the appropriate function based on the specific task.

  Finally, a few comments touch upon the broader context of GNNs within the field of machine learning. One user notes the growing popularity of GNNs and their potential to address complex problems involving relational data. Another commenter draws parallels between GNNs and other deep learning architectures, highlighting the similarities and differences in their underlying principles. This broader perspective helps to situate GNNs within the larger landscape of machine learning and provides context for their development and future directions.