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ogee: Export OSM Road Networks as Graphs from Your Browser
A Chrome extension that turns any OpenStreetMap view into a directed graph — exportable as JSON, GraphML, CSV, or LaTeX TikZ.
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Aspects of OR - Integer Programming (Part 1)
From LP to IP: why integrality matters, the combinatorial explosion, LP relaxations, and why rounding fails.- Published on
Aspects of OR - Integer Programming (Part 2)
Branch and bound: the workhorse algorithm for integer programming, explained with a complete example showing all three pruning types.- Published on
Aspects of OR - Integer Programming (Part 3)
Cutting planes: tightening LP relaxations by slicing off fractional solutions, with Gomory cuts and cover inequalities.- Published on
Aspects of OR - Integer Programming (Part 4)
Branch-and-cut and how modern IP solvers work: combining branch and bound with cutting planes, presolve, heuristics, and parallelism.- Published on
Aspects of OR - Linear Programming (Part 1)
An introduction to linear programming: definitions, standard form, geometric intuition, and practical examples.- Published on
Aspects of OR - Linear Programming (Part 2)
The simplex method explained: slack variables, tableaux, pivoting, degeneracy, and a complete worked example.- Published on
Aspects of OR - Linear Programming (Part 3)
Duality in linear programming: the dual problem, strong duality, complementary slackness, shadow prices, and sensitivity analysis.- Published on
Aspects of OR - Traveling Salesperson Problem - Heuristics (Part 2)
Construction and improvement heuristics for the TSP: nearest neighbor, greedy, 2-opt, 3-opt, and Or-opt.- Published on
Aspects of OR - Traveling Salesperson Problem - Metaheuristics (Part 3)
Metaheuristics for the TSP: simulated annealing, genetic algorithms, and ant colony optimization.- Published on
Network Flows - Part 7
Applications of minimum-cost flows and series conclusion- Published on
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Network Flows - Part 3
Residual graphs and the Max-Flow Min-Cut Theorem- Published on
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Verifying Gallai's Path Conjecture for Small Graphs
We computationally verify Gallai's Path Decomposition Conjecture for all connected graphs with up to 11 vertices, processing over one billion graphs using preprocessing, greedy heuristics, and an ILP solver.- Published on
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Aspects of OR - Traveling Salesperson Problem (TSP)
A brief introduction to the Traveling Salesperson Problem (TSP)- Published on
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Introduction to Graph Theory - Part 2
Basic definitions and first observations and examples- Published on
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Graph Generation with Nauty
In this short article I want to write down the needed steps in order to generate a list of all graphs (no automorphisms!) with nauty.