Spanner constructions focus on the initial design of the network. However, networks tend to
improve over time. In this paper, we focus on the improvement step. Given a graph and a …

In this thesis, we focus on two topics in computational geometry. The first topic is analysing
trajectory similarity. A trajectory tracks the movement of an object over time. A common way …

Let T be a tree with n vertices in a metric space. We consider the problem of adding one
shortcut edge to T to minimize the radius of the resulting graph. For the continuous version of …

Abstract In the k-Diameter-Optimally Augmenting Tree Problem we are given a tree T of n
vertices as input. The tree is embedded in an unknown metric space and we have unlimited …

Let P be a family of paths in a connected graph G so that there exists a uv-path in P for every
choice of vertices u and v. The P-interval J_P (u, v) is the union of vertex sets of all uv-paths …

We consider the problem of augmenting an n-vertex tree with one shortcut in order to
minimize the diameter of the resulting graph. The tree is embedded in an unknown space …

요 약본 논문은 거리 공간 (metric space) 속에 포함된 그래프에서 각 간선의 가중치가 거리 공간
상의 두 끝 정점간의 거리로 주어지는 그래프를 다룬다. 특별히 우리는 이러한 그래프 중 개 …