Methods and problems of wavelength-routing in all-optical networks

We give a survey of recent theoretical results obtained for wavelength-routing in all-optical networks. The survey is based on the previous survey in [Beauquier, B., Bermond, J-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U.: Graph problems arising from wavelength-routing in all-optical networks. In: Proc. of the 2nd Workshop on Optics and Computer Science, part of IPPS'97, 1997]. We focus our survey on the current research directions and on the used methods. We also state several open problems connected with this line of research, and give an overview of several related research directions

On the Effect of Quantum Interaction Distance on Quantum Addition Circuits

We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of qubits and gates of any $\Omega(\log n)$-depth quantum adder circuit for two $n$-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates. Unfortunately, on the chosen $k$-dimensional practical architecture, we prove that the depth lower bound of any exact quantum addition circuits is no longer $\Omega(\log {n})$, but $\Omega(\sqrt[k]{n})$. This result, the first application of graph embedding to quantum circuits and devices, provides a new tool for compiler development, emphasizes the impact of quantum computer architecture on performance, and acts as a cautionary note when evaluating the time performance of quantum algorithms.Comment: accepted for ACM Journal on Emerging Technologies in Computing System

Simulation of Meshes in a Faulty Supercube with Unbounded Expansion

[[abstract]]Reconfiguring meshes in a faulty Supercube is investigated in the paper. The result can readily be used in the optimal embedding of a mesh (or a torus) of processors in a faulty Supercube with unbounded expansion. There are embedding algorithms proposed in this paper. These embedding algorithms show a mesh with any number of nodes can be embedded into a faulty Supercube with load 1, congestion 1, and dilation 3 such that O(n2-w2) faults can be tolerated, where n is the dimension of the Supercube and 2w is the number of nodes of the mesh. The meshes and hypercubes are widely used interconnection architectures in parallel computing, grid computing, sensor network, and cloud computing. In addition, the Supercubes are superior to hypercube in terms of embedding a mesh and torus under faults. Therefore, we can easily port the parallel or distributed algorithms developed for these structuring of mesh and torus to the Supercube.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]KO

Bisection (Band)Width of Product Networks with Application to Data Centers

Abstract. The bisection width of interconnection networks has always been important in parallel computing, since it bounds the amount of information that can be moved from one side of a network to another, i.e., the bisection bandwidth. Finding its exact value has proven to be challenging for some network families. For instance, the problem of finding the exact bisection width of the multidimensional torus was posed by Leighton and has remained open for almost 20 years. In this paper we provide the exact value of the bisection width of the torus, as well as of several d-dimensional classical parallel topologies that can be obtained by the application of the Cartesian product of graphs. To do so, we first provide two general results that allow to obtain upper and lower bounds on the bisection width of a product graph as a function of some properties of its factor graphs. We also apply these results to obtain bounds for the bisection bandwidth of a d-dimensional BCube network, a recently proposed topology for data centers

IST Austria Thesis

Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. Various computationally hard problems were shown to be efficiently solvable for input triangulations that are sufficiently “tree-like.” In this thesis we focus on the key combinatorial parameter in the above context: we consider the treewidth of a compact, orientable 3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered triangulations, we establish quantitative relations between the treewidth and classical topological invariants of a 3-manifold. In particular, among other results, we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold is always within a constant factor of its Heegaard genus

Embedding Schemes for Interconnection Networks.

Graph embeddings play an important role in interconnection network and VLSI design. Designing efficient embedding strategies for simulating one network by another and determining the number of layers required to build a VLSI chip are just two of the many areas in which graph embeddings are used. In the area of network simulation we develop efficient, small dilation embeddings of a butterfly network into a different size and/or type of butterfly network. The genus of a graph gives an indication of how many layers are required to build a circuit. We have determined the exact genus for the permutation network called the star graph, and have given a lower bound for the genus of the permutation network called the pancake graph. The star graph has been proposed as an alternative to the binary hypercube and, therefore, we compare the genus of the star graph with that of the binary hypercube. Another type of embedding that is helpful in determining the number of layers is a book embedding. We develop upper and lower bounds on the pagenumber of a book embedding of the k-ary hypercube along with an upper bound on the cumulative pagewidth