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cs.CG2025
Online Competitive Searching for Rays in the Half-plane
Elmar Langetepe, Florian Gans
We consider the problem of searching for rays (or lines) in the half-plane. The given problem turns out to be a very natural extension of the cow-path problem that is lifted into t…
cs.CG2024
NP-hardness and a PTAS for the Euclidean Steiner Line Problem
Simon Bartlmae, Paul J. Jünger, Elmar Langetepe
The Euclidean Steiner Tree Problem (EST) seeks a minimum-cost tree interconnecting a given set of terminal points in the Euclidean plane, allowing the use of additional intersectio…
cs.CG2024
Simple Grid Polygon Online Exploration Revisited
Maximilian Brock, Martin Brückmann, Elmar Langetepe +1
Due to some significantly contradicting research results, we reconsider the problem of the online exploration of a simple grid cell environment. In this model an agent attains loca…