34549297
Steiner minimal trees for regular polygons
Fifty years ago Jarnik and Kössler showed that a Steiner minimal tree for the vertices of a regularn-gon contains Steiner points for 3 ≤n≤5 and contains no Steiner point forn=6 andn≥13. We complete the story by showing that the case for 7≤n≤12 is the same asn≥13. We also show that the set ofn equally spaced points yields the longest Steiner minimal tree among all sets ofn cocircular points on a given circle.
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.
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).
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.
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.
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.
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.
18860643
The multiroute maximum flow problem revisited
We are given a directed network G = (V, A, u) with vertex setV , arc setA, a source vertexs ∈ V , a destination vertex t ∈ V , a finite capacity vector u = {uij}ij∈A, and a positive integerm ∈ Z+. The multiroute maximum flow problem ( m-MFP) generalizes the ordinary maximum flow problem by seeking a maximum flow from s to t subject to not only the regular flow conservation constraints at the vertices (except s andt) and the flow capacity constraints at the arcs, but also the extra constraints that any flow must be routed alon g m arc-disjoints-t paths. In this paper, we devise two new combinatorial algorithms for m-MFP. One is based on Newton’s method and another is based on augmenting-path technique. We also show how the Newton-based algorithm unifies two existing algorithms, and how the augmen ting-path algorithm is strongly polynomial for case m = 2.
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.
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.
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.