This paper presents a hybrid genetic algorithm to solve the uncapacitated location allocation problems as a combinatorial optimization problem. The proposed method incorporates a modified K-means algorithm that clusters the customers into groups based on the rectilinear distance, and then the initial population of solutions is calculated according to the derived centers of clusters. The hybrid ...

Recently, the inverse connected p-median problem on block graphs G(V,E,w) under various cost functions, say rectilinear norm, Chebyshev and bottleneck Hamming distance. Their contributions include finding a necessary sufficient condition for graphs, developing algorithms showing that these problems can be solved in O(n log n) time, where n is number of vertices underlying graph. Using similar t...

Finding the best rectilinear path with respect to the bends and the lengths of paths connecting two given points in the presence of rectilinear obstacles in a two-layer model is studied in this paper. In this model, rectilinear obstacles on each layer are speciied separately, and the orientation of routing in each layer is xed. An algorithm is presented to transform any problem instance in the ...

In this paper, we deal with arbitrarily shaped rectilinear module placement using the transitive closure graph (TCG) representation. The geometric meanings of modules are transparent to TCG as well as its induced operations, which makes TCG an ideal representation for floorplanning/placement with arbitrary rectilinear modules. We first partition a rectilinear module into a set of submodules and...

The link length of a walk in a multidimensional grid is the number of straight line segments constituting the walk. Alternatively, it is the number of turns that a mobile unit needs to perform in traversing the walk. A rectilinear walk consists of straight line segments which are parallel to the main axis. We wish to construct rectilinear walks with minimal link length traversing grids. If G de...

Given n orthogonal line segments on the plane, their intersection graph is defined such that each vertex corresponds to a segment, and each edge corresponds to a pair of intersecting segments. Although this graph can have f~(n 2) edges, we show that breadth first search can be accomplished in O(n log n) time and O(n) space. As an application, we show that the minimum link rectilinear path betwe...

We prove the following graph coloring result Let G be a connected bipartite planar graph Then one can triangulate G in such a way that the resulting graph is colorable This result implies several new upper bounds for guarding problems including the rst non trivial upper bound for the rectilinear Prison Yard Problem n vertex guards are su cient to watch the interior of a rectilinear polygon with...

We show that the embedding of metric spaces into the l1-grid Z can be characterized in essentially the same fashion as in the case of the l1-plane R . In particular, a metric space can be embedded into Z iff every subspace with at most 6 points is embeddable. Moreover, if such an embedding exists, it can be constructed in polynomial time (for finite spaces) . q 1998 John Wiley & Sons, Inc. Netw...