I’m working on an AI system for territory capture games like Qix or Paper.io where players need to surround empty areas to claim them. My challenge is creating logic that can identify the best spots to target for capturing territory.
In my game setup, I have a 2D grid where blue represents already owned territory and black shows unclaimed space. The AI needs to find optimal paths to enclose these empty regions efficiently.
Basically I need to solve this problem: what’s the most efficient route that can surround the largest possible empty area?
I’ve been thinking about using boundary detection algorithms but I’m not sure if that’s the right approach. Has anyone implemented something similar? What pathfinding techniques work best for this type of enclosure problem?
Been there with a similar project a couple years back. The trick is thinking backwards from the territory you want to capture.
Start by running connected component analysis on your empty regions. This gives you distinct capture targets to evaluate. Then for each region, I used a modified gift wrapping algorithm to find the minimum bounding path that touches your existing territory.
The scoring function is where it gets interesting. I weighted three factors: area gained, path cost, and defensive value. That last one matters more than you think - some captures create better defensive positions for future rounds.
One thing that really helped my AI was implementing a lookahead system. Instead of just evaluating single captures, it considers capture sequences. Sometimes taking a smaller area first opens up a much bigger opportunity next turn.
Also watch out for concave regions. Standard pathfinding can miss efficient routes that cut through narrow gaps. I ended up using a ray casting approach to detect these shortcuts.
The boundary detection idea is solid but use it for preprocessing, not the main algorithm. It helps eliminate obviously bad capture zones early.
In developing my own territory capture AI, I encountered a similar challenge. The goal is to optimize the enclosing of areas while minimizing the path length, akin to the isoperimetric problem. A successful strategy I employed was to implement a flood-fill algorithm to determine connected empty spaces first. I then adapted the A* pathfinding algorithm by adjusting the heuristic to consider both the distance and the area that can be enclosed. This approach helps avoid the pitfalls of purely greedy algorithms, which might overlook larger potential captures that require slightly longer paths. I suggest exploring boundary detection as an initial step to pinpoint potential capture zones, but be sure to integrate robust pathfinding techniques to finalize the enclosure strategy.
yeah, ive tackled this before. use dijkstra’s but tweak the cost function to include perimeter-to-area ratio. you wanna penalize long skinny shapes and favor compact captures. also try a voronoi diagram approach to spot natural territory boundaries first - works gr8 for this stuff.
I ran into this exact problem building a territory AI last year. Treat it as multi-objective optimization, not just pathfinding - that’s the key insight that clicked for me. I used a scanning approach that calculates the convex hull of potential capture zones first, then figures out the minimum perimeter to enclose each region. The algorithm ranks opportunities by area-to-perimeter efficiency while factoring in strategic positioning against existing territory. Here’s what I learned through testing: account for partial captures. Sometimes grabbing a smaller chunk of a large empty area works better if it sets you up for future expansions. Boundary detection is definitely worth exploring, but I’d combine it with dynamic programming to evaluate different enclosure sequences instead of just individual captures.
This reminds me of computational geometry problems I tackled during my master’s thesis. The breakthrough was treating it as constrained optimization instead of pure pathfinding. I built a grid-based potential field where each empty cell gets a capture value based on distance from owned territory and its connected component size. Then I used gradient ascent to find paths that maximize enclosed area vs path length ratio. The game-changer was preprocessing to find ‘bottlenecks’ - narrow passages between larger empty regions. These are goldmines because closing one passage can secure multiple areas at once. For path planning, bidirectional search crushed standard A* variants. You search from your current position and from potential completion points around the target simultaneously. This dodges the local minima that wreck greedy approaches. One gotcha I learned the hard way: always validate your path actually creates a valid enclosure. My early versions would generate paths that looked perfect but had tiny gaps that killed the entire capture.