Given a directed graph G = (N,A) with arc capacities uij and a minimum cost flow problem defined on G, the capacity inverse minimum cost flow problem is to find a new capacity vector û for the arc set A such that a given feasible flow x̂ is optimal with respect to the modified capacities. Among all capacity vectors û satisfying this condition, we would like to find one with minimum ‖û− u‖ value....

This paper is concerned with the problem of locating II new facilities in the median space when there are k facilities already located. The objective is to minimize the weighted sum of distances. Necessary and sufficient conditions are established. Based on these results a polynomial algorithm is presented. The algorithm requires the solution of a sequence of minimum-cut problems. The complexit...

The rectilinear Steiner tree problem asks for a shortest tree connecting given points in the plane with rectilinear distance. The best theoretically analyzed algorithm for this problem with a fairly practical behaviour bases on dynamic programming and has a running time of O(n 2 2:62 n) (Ganley/Cohoon). The best implementation can solve random problems of size 35 (Salowe/Warme) within a day. In...

This paper investigates a multi-period rectilinear distance 1-center location problem considering a lineshaped barrier, in which the starting point of the barrier follows the uniform distribution function. In addition, the existing points are sensitive to demands and locations. The purpose of the presented model is to minimize the maximum barrier distance from the new facility to the existing f...

Electron microscopy of thin-sectioned and freeze-fractured preparations of the cerebellum of the weaver mouse indicates that the dendritic spines are morphologically identical to those of their normal littermates. The weaver dendritic spines have been characterized as "unattached" since the synaptic input from the parallel fibers is absent (8-10). The entire region around the dendritic spines i...

Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least (n 2) time. More eecient approaches nd a minimum spanning tree only among edges in the Delaunay triangulation of the po...

This paper derives the distribution of the difference between the distances to the first and the second nearest facilities. Facilities are represented as points of regular and random patterns, and distance is measured as Euclidean and rectilinear distances on a continuous plane. Since the difference between the distances is regarded as the additional travel distance of customers when the neares...

Given a set of obstacles and two distinguished points in the plane the problem of nding a collision free path subject to a certain optimization function is a fundamental problem that arises in many elds, such as motion planning in robotics, wire routing in VLSI and logistics in operations research. In this survey we emphasize its applications to VLSI design and limit ourselves to the rectilinea...

In this paper, we provide a simple approximation for the distance from an arbitrary location to the kth nearest point. Distance is measured as the Euclidean and the rectilinear distances on a continuous plane. The approximation demonstrates that the kth nearest distance is proportional to the square root of k and inversely proportional to the square root of the density of points. The accuracy o...

We present eecient algorithms for nding rectilinear collision-free paths between two given points among a set of rectilinear obstacles. Our results improve the time complexity of previous results for nding the shortest rectilinear path, the minimum-bend shortest rectilinear path, the shortest minimum-bend rectilinear path and the minimum-cost rectilinear path. For nding the shortest rectilinear...