36724744
A decomposition theorem on Euclidean Steiner minimal trees
The Euclidean Steiner minimal tree problem is known to be an NP-complete problem and current alogorithms cannot solve problems with more than 30 points. Thus decomposition theorems can be very helpful in extending the boundary of workable problems. There have been only two known decomposition theorems in the literature. This paper provides a 50% increase in the reservoir of decomposition theorems.
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.
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).
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.
206027538
A coloring problem on the n-cube
Abstract In this paper, we consider a coloring problem on the n-cube that arises in the study of scalability of optical networks. Let χ k (n) be the minimum number of colors needed to color the vertices of the n-cube so that every two vertices with Hamming distance ⩽k have different colors. We show that for k=3, 2n⩽χ 3 (n)⩽2 ⌈ log 2 n⌉+1 . We also provide upper and lower bounds on χ k (n) for general k.
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.
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.
9933311
The k-Steiner Ratio in the Rectilinear Plane
A Steiner minimum tree (SMT) in the rectilinear plane is the shortest length tree interconnecting a set of points, called the regular points, possibly using additional vertices. Ak-size Steiner minimum tree (kSMT) is one that can be split into components where all regular points are leaves and all components have at mostkleaves. Thek-Steiner ratio in the rectilinear plane, ?k, is the infimum of the ratios SMT/kSMT over all finite sets of regular points. Thek-Steiner ratio is used to determine the performance ratio of several recent polynomial-time approximations for Steiner minimum trees. Previously it was known that in the rectilinear plane, ?2=2/3, ?3=4/5, and (2k?2)/(2k?1)??k(L1)?(2k?1)/(2k) fork?4. In 1991, P. Berman and V. Ramaiyer conjectured that in fact ?k=(2k?1)/(2k) fork?4. In this paper we prove their conjecture.
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.
11088545
Supporting Random Access on Real-Time Retrieval of Digital Continuous Media
In addition to the large data size requirement and real-time constraint in continuous media, future video applications such as video editing demand a random access capability at the video-frame level. This paper introduces our study on effective buffering control for the real-time retrieval of jitter-free digital video medium. We adopt a video-frame level approach to maintaining the flexibility on placement and analysing the efficiency of the buffering schemes. An integrated solution which offers efficient buffering schemes and flexible storage placement to support random access is our goal. We present two buffering schemes: the two-buffer scheme and the k-buffer compensation scheme. The two-buffer scheme requires that all the frames in a block are stored consecutively, while providing random access between blocks. However, this intuitive buffering scheme potentially requires a large block size and buffer space. The k-buffer compensation scheme is proposed to resolve this large buffer space requirement, by using more than two buffers and requiring a minimal number of blocks randomly placed in each cylinder. This scheme differs from the contiguous placement scheme because individual blocks can be stored anywhere in each cylinder. Compared to the two-buffer scheme, the k-buffer compensation scheme requires less buffer space, has higher disk utilization and finer granularity on disk data transfer. The placement requirements are more flexible and implementable than the contiguous and storage pattern placement schemes. Experimental measurement results reveal the significant improvements on the buffer-size reduction and placement flexibility by using the k-buffer compensation scheme. Extensions of the k-buffer compensation scheme to support multiple streams are also addressed.
17041567
On-line scheduling of small open shops
We investigate the problem of on-line scheduling open shops of two and three machines with an objective of minimizing the schedule makespan. We first propose a 1.848-competitive permutation algorithm for the non-preemptive scheduling problem of two machines and show that no permutation algorithm can be better than 1.754-competitive. Secondly, we develop a (27/19)-competitive algorithm for the preemptive scheduling problem of three machines, which is most competitive.