Abstract
We study a continuous facility location problem on undirected graphs where all edges have unit length and where the facilities may be positioned at the vertices as well as at interior points of the edges. The goal is to cover the entire graph with a minimum number of facilities with covering range \(\delta >0\). In other words, we want to position as few facilities as possible subject to the condition that every point on every edge is at distance at most \(\delta \) from one of these facilities.
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