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Given a graph G and a drawing or layout of G, it is sometimes desirable to alter or adjust the layout. The challenging aspect of designing layout adjustment algorithms is to maintain a user's mental picture of the original layout. We present a new approach to layout adjustment called cluster busting in anchored graph drawing. We then give two algorithms as… (More)

We give processor-allocation algorithms for grid architec-tures, where the objective is to select processors from a set of available processors to minimize the average number of communication hops. The associated clustering problem is as follows: Given n points in d , find a size-k subset with minimum average pairwise L1 distance. We present a natural… (More)

EEcient interprocessor communication is crucial to increasing the performance of parallel computers. In this paper, a special framework is developed on the generalized hypercube, a network that is currently receiving considerable attention. Using this framework as the basic tool, a number of spanning graphs with special properties to t various communication… (More)

A k-track drawing is a crossing-free 3D straight-line drawing of a graph G on a set of k parallel lines called tracks. The minimum value of k for which G admits a k-track drawing is called the track number of G. In [18] it is proved that every graph from a proper minor closed family has constant track number if and only if it has constant queue number. In… (More)

Let S and T be two sets of points with total cardinality n. The minimum-cost many-to-many matching problem matches each point in S to at least one point in T and each point in T to at least one point in S, such that sum of the matching costs is minimized. Here we examine the special case where both S and T lie on the line and the cost of matching s ∈ S to t… (More)

We discuss worst-case bounds on the ratio of maximum matching and minimum median values for finite point sets. In particular, we consider " minimum stars, " which are defined by a center chosen from the given point set, such that the total geometric distance L S to all the points in the set is minimized. If the center point is not required to be an element… (More)

D Di ip pa ar rt ti im me en nt to o d di i I In ng ge eg gn ne er ri ia a E El le et tt tr ro on ni ic ca a e e d de el ll l' 'i in nf fo or rm ma az zi io on ne e

Let G be a set of disjoint bi-chromatic straight line segments and H be a set of red and blue points in the plane, no three points are collinear. We give tight upper bounds on the maximum degree of a node in the color conforming minimum weight spanning tree (MST) formed by G and H. We also consider bounds on the total length of the edges of 1) the planar… (More)

A flip or edge-replacement is considered as a transformation by which one edge e of a geometric object is removed and an edge f (f = e) is inserted such that the resulting object belongs to the same class as the original object. In this paper, we consider Hamiltonian planar paths as geometric objects. A technique is presented for transforming a given planar… (More)