7549514
Connectivity of Consecutive-d Digraphs
Abstract The concept of consecutive- d digraph is proposed by Du, Hsu and Hwang. It generalizes the class of de Bruijin digraphs, the class of Imase-Itoh digraphs and the class of generalized de Bruijin graphs. We modify consecutive- d digraphs by connecting nodes with a loop into a circuit and deleting all loops. The result in this paper shows that the link-connectivity or the connectivity of modified consecutive- d digraphs get better.
14358235
New bounds on a hypercube coloring problem
In studying the scalability of optical networks, one problem which arises involves coloring the vertices of the n-cube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of χ??(n), the minimum number of colors needed, appears to be a difficult problem. In this note, we improve the known lower and upper bounds of χ??(n) and indicate the connection of this coloring problem to linear codes.
43203779
The k-Steiner ratio in graphs
A Steiner minimum tree, SMT, is the shortest length tree in a metric space interconnecting a set of points, called the regular points, possibly using additional vertices. A k-size Steiner minimum tree, kSMT, is one that can be split into components where all regular points are leaves and all components have at most k leaves. The k-$lteiner ratio, pk, is the infimum of the ratios SMT/kSMT over all sets of regular points in all possible metric spaces, where the distances are given by a complete graph. Previously only p2 and p3 in graphs had been known exactly, and some bounds where know for the others. In this paper we determine pk exactly for all k.
30354625
A class of full Steiner minimal trees
A Steiner minimal tree for a given set of points in the plane is a tree which interconnects these points using lines of shortest possible total length. We construct an infinite class of trees which are the unique full Steiner minimal trees for their sets of endpoints (vertices of degree one).
36038781
A proof of the Gilbert-Pollak conjecture on the Steiner ratio
LetP be a set ofn points on the euclidean plane. LetLs(P) andLm(P) denote the lengths of the Steiner minimum tree and the minimum spanning tree onP, respectively. In 1968, Gilbert and Pollak conjectured that for anyP,Ls(P)≥(√3/2)Lm(P). We provide a proof for their conjecture in this paper.
2453836
On connectivity of consecutive-d digraphs
The concept of a consecutive-d digraph was proposed by Du, Hsu and Hwang as a generalization of de Bruijn digraphs, Kautz digraphs, and their generalizations given by Imase and Itoh and Reddy, Pradhan and Kuhl. In this paper, we determine the connectivity of consecutive-d digraphs and study how to modify consecutive-d digraphs to reach maximum connectivity. Our results will generalize and improve several existing results on the connectivity of de Bruijn digraphs, Kautz digraphs and Imase-Itoh digraphs.
16833982
The k-level facility location game
We propose a cost-sharing scheme for the k-level facility location game that is cross-monotonic, competitive, and 6-approximate cost recovery. This extends the recent result for the 1-level facility location game of Pal and Tardos.
12802794
A systematic approach to design the network-based learning environment for home and office
An effective network-based learning environment provides synchronous and asynchronous education to learners who are physically, remote from or opt to telecommute to the base location of instruction. The environment provides content creation, user registration, course material storage, multiple delivery means, and end-user viewing tools. An intriguing aspect of the environment is how to model a lecture in terms of pre-, in-, and post-class information. We regard a lecture model collectively as an activity consisting of three elements: lecture materials, lecture presentation, and lecture interaction. We derive the synchronization specification for the media objects and define strong-weak networked hyperlink (SWNH) to represent the lecture structure and inter/intra media object reference in the distributed network environment. The specification and representation exhibit an object-oriented modular design. The presentation of the lecture embody both the event-driven and timeline-based presentation synchronization where the browsing and authoring tools developed earlier fit right into the learning environment, e.g. FLIPS and HQT by the authors, or are immediately available through other providers, e.g. Web browsers.
35793386
An improved algorithm for decomposing arc flows into multipath flows
We consider a multipath maximum flow problem introduced by Kishimoto (Networks 27(4)(1996)279-291). The focus is on efficient transformation from arc flows into multipath flows, where a multipath flow is a nonnegative combination of multipaths. A new algorithm that is more efficient than existing ones is proposed for the transformation.
16471624
Preemptive on-line scheduling for two uniform processors
This paper considers the problem of preemptive on-line scheduling for two uniform processors in which one of the processors has speed 1 and the other has speed s>=1. The objective is to minimize the makespan. A best possible algorithm with competitive ratio of (1+s)^2/(1+s+s^2) is proposed for this problem.
9780632
An integrated admission control scheme for the delivery of streaming media
Quality of service (QoS) assurance is a major concern in media-on-demand (MoD) systems. Admission control is one of the most important issues that need to be addressed for QoS assurance. Also, smoothing is a basic technique for the media server to improve its bandwidth and buffer utilization. However, existing approaches cannot achieve the best resource utilization because (1) they cannot fully utilize the time-varying buffer spaces available at both server and client sides due to the separation of admission control and smoothing processes, and (2) the computing time is unacceptable for media of long duration. In this paper, we formulate the admission control as an integer programming problem and propose several heuristic methods for solving the problem. Specially, we introduce an efficient scheme, called batched admission (BA) scheme, which integrates admission control, transmission rate smoothing, and batching, to achieve best resource utilization with guaranteed QoS. Experimental studies show that the BA scheme outperforms existing approaches.