Ingredients of Locational Analysis (J. Krarup & P. Pruzan). The p-Median Problem and Generalizations (P. Mirchandani). The Uncapacitated Facility Location Problem (G. Cornuejols, et al.). Multiperiod Capacitated Location Models (S. Jacobsen). Decomposition Methods for Facility Location Problems (T. Magnanti & R. Wong). Covering Problems (A. Kolen & A. Tamir). p-Center Problems (G. Handler). Duality: Covering and Constraining p-Center Problems on Trees (B. Tansel, et al.). Locations with Spatial Interactions: The Quadratic Assignment Problem (R. Burkard). Locations with Spatial Interactions: Competitive Locations and Games (S. Hakimi). Equilibrium Analysis for Voting and Competitive Location Problems (P. Hansen, et al.). Location of Mobile Units in a Stochastic Environment (O. Berman, et al.). Index.

https://link.springer.com/content/pdf/10.1057%2Fjors.1991.208.pdf

Discrete location theory

On the order of magnitude of the difference between consecutive prime numbers

Sur le probléme des courbes gauches en Topologie

One way to broadcast a popular/hot video is to let multiple users share a few channels. The stress on the scarce channels can be alleviated without sacrificing viewer waiting time. One common approach is to partition the video into fixed-length segments, which are broadcast on several channels periodically. Two representative approaches are the fast broadcasting scheme and the PAGODA scheme, which can broadcast a video using k channels by having new viewers wait no longer than /spl Theta/(D/2/sup k/) and /spl Theta/(D/5/sup k/2/) time, respectively, where D is the length of the video. In this paper, we propose a new scheme, called recursive frequency splitting (RFS), that significantly improves on existing schemes in terms of viewer waiting time. Some lower bounds on the viewers' waiting time are also developed.

一個適用於熱門視訊服務之遞迴頻率分割廣播策略; A Recursive Frequency-Splitting Scheme for Broadcasting Hot Videos

http://tcs.catholic.ac.kr/%7Ejhpark/papers/panconnectivity_in_RHL1.pdf

Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements

Jwo et al. lNetworks 23 l1993r 315–326r introduced the alternating group graph as an interconnection network topology for computing systems. They showed that the proposed structure has many advantages over n-cubes and star graphs. For example, all alternating group graphs are hamiltonian-connected li.e., every pair of vertices in the graph are connected by a hamiltonian pathr and pancyclic li.e., the graph can embed cycles with arbitrary length with dilation 1r. In this article, we give a stronger result: all alternating group graphs are panconnected, that is, every two vertices x and y in the graph are connected by a path of length k for each k satisfying dlx, yr ≤ k ≤ vVv - 1, where dlx, yr denotes the distance between x and y, and vVv is the number of vertices in the graph. Moreover, we show that the r-dimensional alternating group graph AGr, r ≥ 4, is lr - 3r-vertex fault-tolerant Hamiltonian-connected and lr - 2r-vertex fault-tolerant hamiltonian. The latter result can be viewed as complementary to the recent work of Lo and Chen lIEEE Trans. Parallel and Distributed Systems 12 l2001r 209–222r, which studies the fault-tolerant hamiltonicity in faulty arrangement graphs. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44l4r, 302–310 2004

Panconnectivity, fault-tolerant hamiltonicity and hamiltonian-connectivity in alternating group graphs

The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number of advantages, including the increase of fault-tolerance and bandwidth. Thus, the designs of multiple ISTs on several classes of networks have been widely investigated. Tang et al. [S.-M. Tang, Y.-L. Wang, Y.-H. Leu, Optimal independent spanning trees on hypercubes, Journal of Information Science and Engineering 20 (2004) 143-155] studied the problem of constructing k ISTs on k-dimensional hypercube Q"k, and provided a recursive algorithm for their construction (i.e., for constructing k ISTs of Q"k, it needs to build k-1 ISTs of Q"k"-"1 in advance). This kind of construction forbids the possibility that the algorithm could be parallelized. In this paper, based on a simple concept called Hamming distance Latin square, we design a new algorithm for generating k ISTs of Q"k. The newly proposed algorithm relies on a simple rule and is easy to be parallelized. As a result, we show that the ISTs we constructed are optimal in the sense that both the heights and the average path length of trees are minimized.

/pdf/parallel-construction-of-optimal-independent-spanning-trees-5p7emmogp5.pdf

Parallel construction of optimal independent spanning trees on hypercubes

Two spanning trees rooted at some vertex r in a graph G are said to be independent if for each vertex v of G, v ≠ r, the paths from r to v in two trees are vertex-disjoint A set of spanning trees of G is said to be independent if they are pairwise independent A set of independent spanning trees is optimal if the average path length of the trees is the minimum Any k-dimensional hypercube has k independent spanning trees rooted at an arbitrary vertex In this paper, an O(kn) time algorithm is proposed to construct k optimal independent spanning trees on a k-dimensional hypercube, where n = 2 k is the number of vertices in a hypercube

Optimal Independent Spanning Trees on Hypercubes

This paper is concerned with a particular family of regular 4-connected graphs, called chordal rings. Chordal rings are a variation of ring networks. By adding two extra links (or chords) at each vertex in a ring network, the reliability and fault-tolerance of the network are enhanced. Two spanning trees on a graph are said to be independent if they are rooted at the same vertex, say, r, and for each vertex v \neq r, the two paths from r to v, one path in each tree, are internally disjoint. A set of spanning trees on a given graph is said to be independent if they are pairwise independent. Iwasaki et al. [CHECK END OF SENTENCE] proposed a linear time algorithm for finding four independent spanning trees on a chordal ring. In this paper, we give a new linear time algorithm to generate four independent spanning trees with a reduced height in each tree. Moreover, a complete analysis of our improvements on the heights of independent spanning trees is also provided.

Reducing the Height of Independent Spanning Trees in Chordal Rings

Two spanning trees rooted at vertex r in a graph G are called independent spanning trees (ISTs) if for each vertex v in G, vner, the paths from vertex v to vertex r in these two trees are internally distinct. If the connectivity of G is k, the IST problem is to construct k ISTs rooted at each vertex. The IST problem has found applications in fault-tolerant broadcasting, but it is still open for general graphs with connectivity greater than four. In this paper, we shall propose a very simple algorithm for solving the IST problem on multidimensional torus networks. In our algorithm, every vertex can determine its parent for a specific independent spanning tree only depending on its own label. Thus, our algorithm can also be implemented in parallel systems or distributed systems very easily.

Yue-Li Wang

Papers

Panconnectivity, fault-tolerant hamiltonicity and hamiltonian-connectivity in alternating group graphs

Parallel construction of optimal independent spanning trees on hypercubes

Optimal Independent Spanning Trees on Hypercubes

Reducing the Height of Independent Spanning Trees in Chordal Rings

Independent Spanning Trees on Multidimensional Torus Networks