A Distributed Multicast Routing Algorithm for Real-Time Applications in Wide Area Networks

The problem of constructing a minimal cost multicast routing tree (MRT) with delay constraints in wide area networks (WAN) is considered. A new distributed token-passing based algorithm that constructs a sub-optimal MRT satisfying given delay constraints for all members in the multicast group is presented. In contrast with the previous works by Jia [A distributed algorithm of delay-bounded multicast routing for multimedia applications in wide area networks, IEEE/ACM Trans. Network. 6 (1998) 828–837] and several others [Y. Im, Y. Lee, S. Wi, Y. Choi, Delay constrained distributed multicast routing algorithm, Comput. Comm. 20 (1997) 60–66; X. Jia, Y. Zhang, N. Pissinou, K. Makki, A distributed multicast routing protocol for real-time multicast applications, Comput. Networks 31 (1999) 101–110; Q. Sun, H. Langendorfer, A distributed delay-constrained dynamic multicast routing algorithm, Telecommun. Systems 11 (1999) 47–58], in which cycles may occur, we show that the multicast routing network produced by our algorithm is indeed a tree, namely, cycle free. Also the success rate of our algorithm to find a feasible solution, if one exists, is guaranteed to be 100%, while Jia’s algorithm is not. Furthermore, our algorithm is fault tolerant and can also adapt to cases where the multicast group members are allowed to join or leave the multicast session dynamically. Simulations have been conducted and the results show that the MRT generated by our algorithm has better performance compared to previous methods

An iterative distributed algorithm for multi-constraint multicast routing

In this paper, we propose a group computation based distributed algorithm for solving the problem of multi-constraint multicast routing. This algorithm is fully distributed and can generate within acceptable time and message complexities a multicast routing tree, which not only satisfies the required multiple QoS constraints but also has a sub-optimal network cost. The results of the simulations show that the multicast routing tree generated by our algorithm has better performance than the previous well-known results

On 2-Dimensional Channel Assignment Problem

We consider the 2-dimensional channel assignment problem: given a set S of iso-oriented rectangles (whose sides are parallel to the coordinate axes), find a minimum number of planes (channels) to which only nonoverlapping rectangles are assigned. This problem is equivalent to the coloring problem of the rectangle intersection graph G = (V, E), in which each vertex in V corresponds to a rectangle and two vertices are adjacent iff their corresponding rectangles overlap, and we ask for an assignment of a minimum number of colors to the vertices such that no adjacent vertices are assigned the same color. We show that the problem is NP-hard

Visibility of a Simple Polygon

The hidden line problem in the plane is studied and an optimal algorithm for finding the visibility polygon of a point inside or outside a simple polygon is given. The algorithm uses only one stack, instead of three as used in a previously known algorithm by El-Gindy and Avis (J. Algor.2, 1981, 186–197). As a result, the algorithm is simpler to implement and easier to understand and its correctness can be easily verified

A New Approach for the Geodesic Voronoi Diagram of Points in a Simple Polygon and Other Restricted Polygonal Domains

We introduce a new method for computing the geodesic Voronoi diagram of point sites in a simple polygon and other restricted polygonal domains. Our method combines a sweep of the polygonal domain with the merging step of a usual divide-and-conquer algorithm. The time complexity is O((n+k) log(n+k)) where n is the number of vertices and k is the number of points, improving upon previously known bounds. Space is O(n+k) . Other polygonal domains where our method is applicable include (among others) a polygonal domain of parallel disjoint line segments and a polygonal domain of rectangles in the L 1 metric

On k-Nearest Neighbor Voronoi Diagrams in the Plane

The notion of Voronoi diagram for a set of N points in the Euclidean plane is generalized to the Voronoi diagram of order k and an iterative algorithm to construct the generalized diagram in 0(k2N log N) time using 0(k2(N − k)) space is presented. It is shown that the k-nearest neighbor problem and other seemingly unrelated problems can be solved efficiently with the diagram