7236819
Creating a virtual network laboratory
Networking courses are traditionally conceptual in nature, with little opportunity for students to apply what they have learned in order to strengthen their knowledge. To support these courses, the University of Minnesota established a hands-on network laboratory. Educational and operational concerns have surfaced throughout the years due to the physical laboratory constraints and difficulty of satisfying the high demand. To address these issues, and to overcome the shortcomings of current approaches, we are developing a virtual network laboratory environment to eliminate most of the constraints, though it is not necessarily replacing all of the physical settings at once. The kernel consists of a collection of online multimedia learning modules which integrate the key laboratory devices with instructional material. The modules are designed to allow students to carry out hands-on networking in a virtual environment or through remote access. This virtual laboratory is easily accessible over the Internet.
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.
16666020
On-line Network Synthesis
We consider on-line network synthesis problems. Let N = {1, , n} be a set of n sites. Trafﬁc ﬂow requirements between pairs of sites are revealed one by one. Whenever a new request rij = rji (i < j) between sites i and j is revealed, an on-line algorithm must install the additional necessary capacity without decreasing the existing network capacity such that all the trafﬁc requirements are met. The objective is to minimize the total capacity installed by the algorithm. The performance of an on-line algorithm is measured by the competitive ratio, deﬁned to be the worst-case ratio between the total capacity by the on-line algorithm and the total optimal (off-line) capacity assuming we have priori information on all the requirements initially. We distinguish between two on-line versions of the problem depending on whether the entire set of sites is known a prior or not. For the ﬁrst version where the entire set of site is unknown, we present a best possible algorithm along with a matching lower bound. For the second version where the entire set of sites is known a priori, we present a best possible algorithm for n ≤ 6. 
 
Key words: On-line algorithm; Approximation algorithm; Network synthesis; Competitive analysis
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.
33293485
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-Steiner ratio, $\rho_{k}$, is the infimum of the ratios SMT/kSMT over all finite sets of regular points in all possible metric spaces, where the distances are given by a complete graph. Previously, only $\rho_{2}$ and $\rho_{3}$ were known exactly in graphs, and some bounds were known for other values of k. In this paper, we determine $\rho_{k}$ exactly for all k. From this we prove a better approximation ratio for the Steiner tree problem in graphs.
8483483
Lower bounds on the minus domination and k-subdomination numbers
A three-valued function f defined on the vertex set of a graph G=(V,E), f:V → {-1,0,1} is a minus dominating function if the sum of its function values over any closed neighborhood is at least one. That is, for every v ∈ V, f(N[v]) ≥ 1, where N[v] consists of v and all vertices adjacent to v. The weight of a minus function is f(V)= Σv ∈ V f(v). The minus domination number of a graph G, denoted by γ-(G), equals the minimum weight of a minus dominating function of G. In this paper, sharp lower bounds on minus domination of a bipartite graph are given. Thus, we prove a conjecture proposed by Dunbar et al. (Discrete Math. 199 (1999) 35), and we give a lower bound on γks(G) of a graph G.
39689433
On 1-rate Wide-sense Nonblocking for 3-stage Clos Networks
Abstract This paper considers the multirate environment in which each network link has a unity capacity and each call is associated with a rate w, 1 ⩾ w>0. The multirate environment is reduced to the 1 -rate environment if all rates are identical. Circuit switching is a special case of 1 -rate in which the constant rate is w = 1. We establish some general relations between wide-sense nonblocking in circuit switching and 1-rate wide-sense nonblocking for the 3-stage Clos network. We also give necessary and sufficient conditions for a 3-stage Clos network with two input switches and two output switches to be wide-sense nonblocking, and give a necessary condition when there are three input switches and three output switches. We conjecture that 1-rate wide-sense nonblocking implies circuit switching wide-sense nonblocking and give some partial evidence.