Network Connectivity Analysis and Optimal Path Planning with PostGIS and pgRouting
Extension Installation
pgRouting requires PostGIS as a prerequisite dependency.
Cloud Hosting
For systems with existing PostgreSQL and PostGIS installations:
sudo apt install postgresql-9.3-pgrouting
Windows Systems
Download from: http://download.osgeo.org/postgis/windows/
Creating Extensions
Enable the required extensions in your PostgreSQL d ...
Posted on Mon, 03 Aug 2026 16:42:10 +0000 by ridiculous
Finding the Shortest Path with Time-Based Road Closures using Dijkstra's Algorithm
This problem involves finding the shrotest path in a graph where certain edges are temporarily closed. The graph has $N$ nodes and $M$ edges, with $N \le 1000$ and $M \le 10000$. Given the constraints, an adjacency matrix is a suitable choice for representing the graph.
We need to determine the optimal travel time for a character, let's call th ...
Posted on Tue, 28 Jul 2026 17:09:19 +0000 by lar5
Advanced Algorithmic Patterns: Interval Games, State-Space Routing, and Lazy Segment Trees
Interval Game Theory via Dynamic Programming
Two participants alternately extract characters from either end of a string. Assuming optimal play from both sides, the objective is to predict the final match outcome. The input guarantees an even-length string, with cumulative lengths capped at 2000 across all test cases.
The problem resolves effic ...
Posted on Tue, 14 Jul 2026 16:35:22 +0000 by ozzysworld
Shortest Path with Time-Based Road Blockages
Problem Overview
Given a graph with (n) intersections ((n \le 10^3)) and (m) bidirectional roads ((m \le 10^4)), a person named T moves first along a predetermined path (c_1, c_2, \ldots, c_g). Each road has a travel time (f[u][v]).
When T traverses a road, that road becomes blocked for the entire duration of T's crossing. Luka starts from inte ...
Posted on Tue, 23 Jun 2026 17:27:31 +0000 by Nick~C
Graph Theory: Shortest Path Algorithms
No difference between shortest paths in directed and undirected graphs (undirected graph are special cases of directed graphs)
Graph storage: dense graphs (adjacency matrix) && sparse graphs (adjacency list)
I. Single-Source Shortest Path
1. All edge weights are positive - Dijkstra's Algorithm
Handling multiple edges and self-loops
...
Posted on Sat, 20 Jun 2026 17:06:21 +0000 by PHP Newb
Finding Shortest Paths with Alternating Edge Colors in Directed Graphs
Given a directed graph with nodes labeled 0 through n-1, where edge are colored either red or blue and may include self-loops and parallel edges.
Each [i, j] pair in red_edges represents a red directed edge from node i to node j. Similarly, each [i, j] pair in blue_edges represents a blue directed edge from node i to node j.
Compute an array re ...
Posted on Wed, 03 Jun 2026 17:06:15 +0000 by sharyn
All-Pairs Shortest Path Computation Using the Floyd-Warshall Method
The Floyd-Warshall algorithm solves the all-pairs shortest path problem in a weighted graph, handling both positive and negative edge weights (with no negative cycles). It uses dynamic programming to iteratively improve shortest path estimates between every pair of vertices.
Core Principal
Define dist[i][j][k] as the shortest distance from node ...
Posted on Fri, 15 May 2026 09:39:48 +0000 by Rovas
Finding the Most Popular Person by Gender Using Floyd-Warshall Algorithm
Problem Analysis
Given N people with known gender (F for female, M for male), each person provides direct distance measurements to their friends. The distance between any two people is the minimum possible distance through any path of known relationships. For each person i, define their "opposite-gender distance" as the maximum value ...
Posted on Tue, 12 May 2026 20:41:56 +0000 by Salkcin