Jean-Lou De Carufel

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Let P be a closed simple polygon with n vertices. For any two points in P , the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P . The geodesic center of P is the unique point in P that minimizes the largest geodesic distance to all other points of P . In 1989, Pollack, Sharir and Rote(More)
We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic bounds were known for the optimal competitive ratio achievable by any search strategy in the worst case. We present the(More)
We present tight upper and lower bounds on the spanning ratio of a large family of θ-graphs. We show that θgraphs with 4k+2 cones (k ≥ 1 and integer) have a spanning ratio of 1 + 2 sin(θ/2), where θ is 2π/(4k + 2). We also show that θ-graphs with 4k + 4 cones have spanning ratio at least 1 + 2 tan(θ/2) + 2 tan(θ/2), where θ is 2π/(4k + 4). This is somewhat(More)
The Fréchet distance is a well studied and commonly used measure to capture the similarity of polygonal curves. Unfortunately, it exhibits a high sensitivity to the presence of outliers. Since the presence of outliers is a frequently occurring phenomenon in practice, a robust variant of Fréchet distance is required which absorbs outliers. We study such a(More)
We seek to augment a geometric network in the Euclidean plane with shortcuts to minimize its continuous diameter, i.e., the largest network distance between any two points on the augmented network. Unlike in the discrete setting where a shortcut connects two vertices and the diameter is measured between vertices, we take all points along the edges of the(More)
We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic bounds were known for the optimal competitive ratio achievable by any search strategy in the worst case. We present the(More)
Let G be a graph, s ∈ G be a source node and t ∈ G be a target node. The sequence of adjacent nodes (graph walk) visited by a routing algorithm is a c-competitive route if its length in G is at most c times the length of the shortest path from s to t in G. We present 21.766-, 17.982and 15.479-competitive online routing algorithms on the Delaunay(More)
We present results on executing point location queries in well-shaped meshes in R and R using the Jumpand-Walk paradigm. If the jump step is performed on a nearest-neighbour search structure built on the vertices of the mesh, we demonstrate that the walk step can be performed in guaranteed constant time. Constant time for the walk step holds even if the(More)