We analyze and visualize collaboration within the Computational Geometry community by modeling co-authorship relations as a graph, where nodes correspond to individual researchers and edges represent shared publications. By aggregating and time-slicing conference data, we construct a dynamic representation of the community that supports both interactive visualization and structured search.

Motivated by applications for robust guarding, we consider a variant of the multiple-watchmen problem that ensures that every point within a polygon P is seen from more than one direction: we search for two routes W₁,W₂, such that every point p ∈ P is contained in a segment w₁w₂ ⊆ P such that w₁ ∈ W₁ and w₂ ∈ W₂. We call such routes segment watchman routes. We show that finding the two routes that are optimal with respect to the min-max criterion is weakly NP-hard even in simple polygons, and that finding the routes that are optimal with respect to the min-sum criterion is NP-hard in polygons with holes. Moreover, we present sufficient conditions for routes to be segment watchman routes, and provide a polynomial-time 2-approximation under both the min-max criterion and the min-sum criterion, both in simple polygons. Finally, we show how to generalize our results for k watchmen.

Let P be a set of n = 2 m + 1 points in the plane in general position. We define the graph G M P whose vertex set is the set of all plane matchings on P with exactly m edges. Two vertices in G M P are connected if the two corresponding matchings have m − 1 edges in common. In this work we show that G M P is connected and give an upper bound of O ( n 2 ) on its diameter. Moreover, we present a lower bound of n − 2 and an upper bound of 2 n − 2 for the diameter of G M P for P in convex position.