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We describe a uniied framework for representing and manipulating binary topological relationships between complex regions, which are arbitrary compositions of homogeneous 2-dimensional surfaces, possibly with holes. Previously, compositions of regions and regions with holes were treated separately and in a restrictive scenario, where it is required that the… (More)

We are given a set of n d-dimensional (possibly intersecting) isothetic hyperrectangles. The topic of this paper is the separation of these rectangles by means of a cutting isothetic hyperplane. Thereby we assume that a rectangle which is intersected by the cutting plane is cut into two non-overlapping hyperrectangles. We investigate the behavior of several… (More)

- V H Nguyen, S Kedad-Sidhoum, M Labbé, G Laporte, I M Martin, J J S Gonzalez
- 2006

In the Ring Star Problem(RSP) the aim is to locate a simple cycle through a subset of vertices of a graph with the objectives of minimizing the sum of two costs: a routing cost proportional to the length of the cycle, and an assignment cost from the vertices not in the cycle to their closest vertex on the cycle. The cycle must pass through some central… (More)

The notion of staircase separator, introduced in 2], greatly facilitates the design of divide-and-conquer algorithms for problems on rectangles. We generalize the concept of staircase separator to k-perfect staircase separator, namely a set of staircase separators which partitions a set S of n axis-parallel, disjoint rectangles into k subsets of (almost)… (More)

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