We investigate the farthest-site Voronoi diagram of k point sites with respect to the geodesic distance in a polygonal domain of n corners and h (≥ 0) holes. In the case of h=0, Aronov et al. [2] in 1993 proved that there are at most O(k) faces in the diagram and the complexity of the diagram is at most O(n+k). However, any nontrivial upper bound on the geodesic farthest-site Voronoi diagram in a polygonal domain when h > 0 remains unknown afterwards. In this paper, we show that the diagram in a polygonal domain consists of Θ(hk) faces and its total combinatorial complexity is Θ(nk) in the worst case for any h ≥ 1. Interestingly, the worst-case complexity of the diagram is independent from the number h of holes if h ≥ 1 while the maximum possible number of faces is dependent on h rather than on the complexity n of the polygonal domain. Also, we present an O(nk log2(n+k) log k)-time algorithm that constructs the diagram explicitly.

Abstract In this article we study a variant of broadcasting: each node has a predetermined ordered list of neighbors regardless of the node, called the source, from which the originating message is transmitted to all nodes in a network. Each node transmits a received message to its neighbors in order of the list. We propose a new measure of the efficiency of a Broadcasting scheme, which is obtained from competitive analysis, and we design new broadcasting schemes for lines, completek‐ary trees, grids, complete graphs, and hypercubes. In particular, we provide optimal broadcasting schemes for lines and grids. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45(4), 224–231 2005

Visibility-based pursuit-evasion problems are as follows: given a polygonal region, one or more searchers with visibility, and an unpredictable intruder that is arbitrarily faster than the searcher, plan the motion of the searchers so as to see the intruder.In this paper, we consider several visibility-based pursuit-evasion problems with a single searcher: l Given a simple polygon with a door (i.e., penetrable vertex) d, can a searcher find an intruder within the polygon in such a way that the intruder couldn't make a dash for the door d? l Given a simple polygon with a door d, can a searcher make no undetected intruder remain in the polygon (that is, find the intruder or evict it from the polygon through d)? l Given a building (represented as a sequence of simple polygons joined by staircases), can the searcher find the intruder within it?For each of the three problems above, we give a characterization of the class of regions that admits a search strategy and present an O(n2)-time algorithm for constructing a search path, if one exists, for an n-sided region.Interestingly, our characterizations imply that each of the above regions searchable by a searcher with omnidirectional vision (i.e., 360' vision) is also searchable by a searcher with two flashlights (i.e., ray visions).As a by-product, we improves the time complexity of the corridor search problem in [2], by a factor of log n. *This work was partially supported by KOSEF 98-0102-07-01-3.permission lo make digital or hard copies of all

In this paper, we consider the problem of nonpreemptively scheduling independent jobs so as to minimize overall finish time on an m-dimensional hypercube system. This problem is NP-hard. We propose a polynomial time approximation algorithm and prove that the absolute performance ratio of the algorithm does not exceed 1.875. This is the first algorithm achieving an absolute performance ratio less than two by a constant.

We present a new ray classification scheme that considerably reduces memory consumption while preserving its inherent time efficiency. Our key idea is due to the fact that the rays lying on the same line are duplicated over many cells in the ray classification scheme. We are thus able to lower the dimensions of the ray space by classifying lines instead of rays. Our scheme produces much simpler-shaped, compact ray cells that eventually accelerate ray shooting operations.

We consider searching problems in robotics that a robot has to find a path to a target by traveling in an unknown starshaped polygon P. The goal is to minimize the ratio of the distance traveled by the robot to the length of the shortest start-to-target path.Let s be a starting point in P. We first present a competitive strategy to find a path from s to the closest kernel point k of P. The length of the path that the robot generates is less than 1 + 2W (< 3.829) times the distance from s to k, which improves the best previous bound 5. 331 [3].Second, given a specified target t in P, we present a competitive strategy to find a path from s to t whose length does not exceed 17 times the length of the shortest s-t path.

A hypermesh, a versatile parallel architecture, is obtained from a 2-dimensional mesh by replacing each linear connection with a hyper-edge. We optimally embed multiple graphs into a hypermesh by a labeling strategy. This optimal embedding provides an optimal expansion, dilation and congestion at the same time. First, we label on an N-node graph G, possibly disconnected, such that this labeling makes it possible to optimally embed multiple copies of G into an N'/spl times/N' hypermesh when N' is divisible by N. Second, we show that many important classes of graphs have this labeling: for example, tree, cycle, mesh of trees and product graphs including mesh, torus, and hypercube. Third, we generalize these results to optimally embed multiple graphs into a multidimensional and possibly non-square hypermesh. This labeling strategy is applicable to the embeddings of other classes of graphs into a hypermesh.

This paper presents a new image morphing method using a two-dimensional deformation technique which provides an intuitive model for a warp. The deformation technique derives aC1-continuous and one-to-one warp from a set of point pairs overlaid on two images. The resulting in-between image precisely reflects the correspondence of features specified by an animator. We also control the transition behaviour in a metamorphosis sequence by taking another deformable surface model, which is simpler and thus more efficient than the deformation technique for a warp. The proposed method separates transition control from feature interpolation and is easier to use than the previous techniques. The multigrid relaxation method is employed to solve a linear system in deriving a warp or transition rates. This method makes our image morphing technique fast enough for an interactive environment.

This paper describes an image metamorphosis technique to handle scattered feature constraints specified with points, polylines, and splines. Solutions to the following three problems are presented: feature specification, warp generation, and transition control. We demonstrate the use of snakes to reduce the burden of feature specification. Next, we propose the use of multilevel free-form deformations (MFFD) to compute C/sup 2/-continuous and one-to-one mapping functions among the specified features. The resulting technique, based on B-spline approximation, is simpler and faster than previous warp generation methods. Furthermore, it produces smooth image transformations without undesirable ripples and foldovers. Finally, we simplify the MFFD algorithm to derive transition functions to control geometry and color blending. Implementation details are furnished and comparisons among various metamorphosis techniques are presented.

This paper presents new solutions to the following three problems in image morphing: feature specification, warp generation, and transition control.To reduce the burden of feature specification, we first adopt a computer vision technique called snakes.We next propose the use of multilevel free-form deformations (MFFD) to achieve C 2 -continuous and one-to-one warps among feature point pairs.The resulting technique, based on B-spline approximation, is simpler and faster than previous warp generation methods.Finally, we simplify the MFFD method to construct C 2 -continuous surfaces for deriving transition functions to control geometry and color blending.

Abstract Broadcasting refers to the process of dissemination of a set of messages originating from one node to all other nodes in a communication network. We assume that, at any given time, a node can transmit a message along at most one incident link and simultaneously receive a message along at most one incident link. We first present an algorithm for determining the amount of time needed to broadcastkmessages in an arbitrary tree. Second, we show that, for everyn, There exists a graph withnnodes whosek‐message broadcast time matches the trivial lower bound ⌈ logn⌉ +k− 1 by designing a broadcast scheme for complete graphs. We call those graphs minimal broadcast graphs. Finally, we construct annnode minimal broadcast graph with fewer than (⌈logn⌉ + 1)2⌈ logn⌉ −1edges.

This paper presents a new image morphing technique using deformable surfaces. Drawbacks of previous techniques are overcome by a physically-based approach which provides an intuitive model for a warp. A warp is derived by two deformable surfaces which specify horizontal and vertical displacements of points on an image. This paper also considers the control of transition behavior in a metamorphosis sequence. The presented technique separates the transition control from interpolating features making it much easier to use than the previous techniques. The multigrid relaxation method is used to compute a deformable surface for a warp or transition rates. This method makes the presented image morphing technique fast enough for an interactive environment.>

This paper begins by giving a characterization of t1/ t1—diagnosable systems. Then a class of t0-diagnosable systems, denoted by d(n,t0,X), is considered. It is shown for any member of this class that: 1) necessary and sufficient conditions for t1/t1—diagnosability are greatly simplified, 2) optimal diagnosis algorithms of time complexity 0(nt0) exist, and most importantly, 3) given the test results, any set F of faults with |F| ≤ t1 can be identified to within a set F' with F ⊆ F' and |F'| ≤ min {t1, |F| + 1}.