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The primary objective of this paper is to introduce the adaptive highways algorithm, a path planning algorithm for vehicles moving on a grid. We consider a workspace that consists of a symmetric grid and a large number of vehicles that move on the grid to ...
In this paper, we propose an efficient planarization algorithm and a routing algorithm dedicated to Unit Disk Graphs whose nodes are localized using the Virtual Raw Anchor Coordinate system (VRAC). Our first algorithm computes a planar 2-spanner under ligh ...
Graph matching is a generalization of the classic graph isomorphism problem. By using only their structures a graph-matching algorithm finds a map between the vertex sets of two similar graphs. This has applications in the de-anonymization of social and in ...
We study complexity and approximation of MIN WEIGHTED NODE COLORING in planar, bipartite and split graphs. We show that this problem is NP-hard in planar graphs, even if they are triangle-free and their maximum degree is bounded above by 4. Then, we prove ...
We propose a computational design approach to generate 3D models composed of interlocking planar pieces. We show how intricate 3D forms can be created by sliding the pieces into each other along straight slits, leading to a simple construction that does no ...
We consider a set V of elements and an optimization problem on V: the search for a maximum (or minimum) cardinality subset of V verifying a given property a"similar to. A d-transversal is a subset of V which intersects any optimum solution in at least d el ...
We study two decomposition problems in combinatorial geometry. The first part of the thesis deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-decomposable if there is a constant m such that any m-fold coveri ...
